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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Geo X Midterm Exam Review Packet
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 1. Name a fourth point in plane TUW.
a. Y b. Z c. W d. X
____ 2. Name the ray in the figure.
a. BA→
b. AB→←
c. BA d. AB→
____ 3. Find AC.
a. 14 b. 15 c. 12 d. 4
____ 4. If EF = 2x − 12, FG = 3x − 15, andEG = 23, find the values of x, EF, and FG. The drawing is not to scale.
a. x = 10, EF = 8, FG = 15 c. x = 10, EF = 32, FG = 45b. x = 3, EF = –6, FG = –6 d. x = 3, EF = 8, FG = 15
____ 5. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale.
a. x = 5, ST = 45 c. x = 10, ST = 60b. x = 5, ST = 60 d. x = 10, ST = 45
Name: ________________________ ID: A
1
____ 6. If m∠BOC= 27 and m∠AOC= 47, then what is the measure of ∠AOB? The diagram is not to scale.
a. 74 b. 40 c. 20 d. 54
____ 7. If m∠DEF = 122, then what are m∠FEG and m∠HEG? The diagram is not to scale.
a. m∠FEG = 122, m∠HEG = 58 c. m∠FEG = 68, m∠HEG = 122b. m∠FEG = 58, m∠HEG = 132 d. m∠FEG = 58, m∠HEG = 122
____ 8. Name an angle supplementary to ∠EOD.
a. ∠BOC b. ∠BOE c. ∠DOC d. ∠BOA
____ 9. Supplementary angles are two angles whose measures have sum ____.Complementary angles are two angles whose measures have sum ____.a. 90; 180 b. 90; 45 c. 180; 360 d. 180; 90
Name: ________________________ ID: A
3
____ 10. The complement of an angle is 25°. What is the measure of the angle?a. 75° b. 155° c. 65° d. 165°
____ 11. ∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5, and m∠JKL = x − 9. Find the measure of each angle.a. ∠DFG = 47, ∠JKL = 53 c. ∠DFG = 52, ∠JKL = 48b. ∠DFG = 47, ∠JKL = 43 d. ∠DFG = 52, ∠JKL = 38
____ 12. ∠1 and ∠2 are supplementary angles. m∠1 = x − 39, and m∠2 = x + 61. Find the measure of each angle.a. ∠1 = 79, ∠2 = 101 c. ∠1 = 40, ∠2 = 150b. ∠1 = 40, ∠2 = 140 d. ∠1 = 79, ∠2 = 111
____ 13. MO→
bisects ∠LMN, m∠LMO = 8x − 23, and m∠NMO = 2x + 37. Solve for x and find m∠LMN. The diagram is not to scale.
a. x = 9, m∠LMN = 98 c. x = 10, m∠LMN = 114b. x = 9, m∠LMN = 49 d. x = 10, m∠LMN = 57
____ 14. Find the circumference of the circle in terms of π.
a. 156π in. b. 39π in. c. 1521π in. d. 78π in.
Name: ________________________ ID: A
4
____ 15. Find the area of the circle in terms of π.
a. 30π in.2 b. 900π in.2 c. 60π in.2 d. 225π in.2
____ 16. The figure is formed from rectangles. Find the total area. The diagram is not to scale.
a. 104 ft 2 b. 36 ft 2 c. 80 ft 2 d. 68 ft 2
____ 17. If the perimeter of a square is 72 inches, what is its area?
a. 72 in.2 b. 324 in.2 c. 18 in.2 d. 5,184 in.2
____ 18. Name the Property of Equality that justifies the statement:If p = q, then p − r = q − r.a. Reflexive Property c. Symmetric Propertyb. Multiplication Property d. Subtraction Property
____ 19. Name the Property of Congruence that justifies the statement:
If XY ≅ WX, thenWX ≅ XY.a. Symmetric Property c. Reflexive Propertyb. Transitive Property d. none of these
____ 20. Name the Property of Congruence that justifies the statement:If ∠A ≅ ∠B and∠B ≅ ∠C, then∠A ≅ ∠C.a. Transitive Property c. Reflexive Propertyb. Symmetric Property d. none of these
Name: ________________________ ID: A
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Use the given property to complete the statement.
____ 21. Transitive Property of Congruence
If CD ≅ EF andEF ≅ GH , then ______.
a. EF ≅ GH c. CD ≅ GH
b. EF ≅ EF d. CD ≅ EF
____ 22. Find the value of x.
a. –19 b. 125 c. 19 d. 55
____ 23. m∠3 = 37. Find m∠1.
a. 37 b. 143 c. 27 d. 153
Name: ________________________ ID: A
6
____ 24. Find the values of x and y.
a. x = 15, y = 17 c. x = 68, y = 112b. x = 112, y = 68 d. x = 17, y = 15
____ 25. Which angles are corresponding angles?
a. ∠8and∠16 c. ∠4and∠8b. ∠7and∠8 d. none of these
____ 26. Line r is parallel to line t. Find m∠5. The diagram is not to scale.
a. 45 b. 35 c. 135 d. 145
Name: ________________________ ID: A
7
____ 27. Find the value of the variable if m Ä l, m∠1 = 2x + 44 and m∠5 = 5x + 38. The diagram is not to scale.
a. 1 b. 2 c. 3 d. –2
____ 28. Complete the statement. If a transversal intersects two parallel lines, then ____.a. corresponding angles are supplementaryb. same-side interior angles are complementaryc. alternate interior angles are congruentd. none of these
____ 29. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary.a. acute c. same-side interiorb. alternate interior d. corresponding
____ 30. Which lines, if any, can you conclude are parallel given that m∠1 + m∠2 = 180? Justify your conclusion with a theorem or postulate.
a. j Ä k , by the Converse of the Same-Side Interior Angles Theoremb. j Ä k , by the Converse of the Alternate Interior Angles Theoremc. g Ä h, by the Converse of the Alternate Interior Angles Theoremd. g Ä h, by the Converse of the Same-Side Interior Angles Theorem
Name: ________________________ ID: A
8
____ 31. m∠1 = 6x andm∠3 = 120. Find the value of x for p to be parallel to q. The diagram is not to scale.
a. 114 b. 126 c. 120 d. 20
____ 32. If c ⊥ b and a Ä c, what is m∠2?
a. 90 c. 74b. 106 d. not enough information
____ 33. Find the value of k. The diagram is not to scale.
a. 17 b. 73 c. 118 d. 107
Name: ________________________ ID: A
9
____ 34. Find the values of x, y, and z. The diagram is not to scale.
a. x = 86, y = 94, z = 67 c. x = 67, y = 94, z = 86b. x = 67, y = 86, z = 94 d. x = 86, y = 67, z = 94
____ 35. Classify the triangle by its sides. The diagram is not to scale.
a. straight b. scalene c. isosceles d. equilateral
____ 36. Classify ∆ABC by its angles, when m∠A = 32, m∠B = 85, and m∠C = 63.a. right b. straight c. obtuse d. acute
____ 37. Find the value of x. The diagram is not to scale.
a. 33 b. 162 c. 147 d. 75
Name: ________________________ ID: A
10
____ 38. Find the value of the variable. The diagram is not to scale.
a. 66 b. 19 c. 29 d. 43
____ 39. How many sides does a regular polygon have if each exterior angle measures 20?a. 17 sides b. 20 sides c. 21 sides d. 18 sides
____ 40. The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third exterior angle?a. 75 b. 115 c. 105 d. 95
____ 41. Use less than, equal to, or greater than to complete the statement. The measure of each exterior angle of a regular 7-gon is ____ the measure of each exterior angle of a regular 5-gon.a. cannot tell b. equal to c. less than d. greater than
____ 42. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.
a. n − 2180
b. (n − 1)180 c. 180n − 1
d. (n − 2)180
____ 43. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____.
a. (n – 2)180 b. 360 c.(n − 2)180
nd. 180n
Name: ________________________ ID: A
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____ 44. Justify the last two steps of the proof.
Given: RS ≅ UT and RT ≅ USProve: ∆RST≅ ∆UTS
Proof:
1. RS ≅ UT 1. Given
2. RT ≅ US 2. Given
3. ST ≅ TS 3. ?
4. ∆RST≅ ∆UTS 4. ?
a. Symmetric Property of ≅; SSS c. Reflexive Property of ≅; SSSb. Reflexive Property of ≅; SAS d. Symmetric Property of ≅; SAS
____ 45. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?a. c.
b. d.
Name: ________________________ ID: A
12
____ 46. From the information in the diagram, can you prove ∆FDG ≅ ∆FDB? Explain.
a. yes, by ASA c. yes, by SASb. yes, by AAA d. no
____ 47. Based on the given information, what can you conclude, and why?
Given: ∠H ≅ ∠L, HJ ≅ JL
a. ∆HIJ ≅ ∆LKJ by ASA c. ∆HIJ ≅ ∆JLK by ASAb. ∆HIJ ≅ ∆JLK by SAS d. ∆HIJ ≅ ∆LKJ by SAS
____ 48. Name the theorem or postulate that lets you immediately conclude ∆ABD ≅ ∆CBD.
a. SAS b. ASA c. AAS d. none of these
Name: ________________________ ID: A
13
____ 49. Supply the missing reasons to complete the proof.
Given: ∠Q ≅ ∠T and QR≅ TR
Prove: PR ≅ SR
Statement Reasons
1. ∠Q ≅ ∠T and
QR ≅ TR1. Given
2. ∠PRQ ≅ ∠SRT 2. Vertical angles are congruent.
3. ∆PRQ ≅ ∆SRT 3. ?
4.PR ≅ SR 4. ?
a. ASA; Substitution c. AAS; CPCTCb. SAS; CPCTC d. ASA; CPCTC
____ 50. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?
a. 71° b. 142° c. 152° d. 76°
____ 51. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?a. 69° b. 84° c. 138° d. 96°
Name: ________________________ ID: A
14
____ 52. Find the value of x. The diagram is not to scale.
a. 32 b. 50 c. 64 d. 80
____ 53. Find the value of x.
a. 4 b. 8 c. 6.6 d. 6
____ 54. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale.
a. 27 b. 3 c. 15 d. 30
Name: ________________________ ID: A
15
____ 55. What is the name of the segment inside the large triangle?
a. perpendicular bisector c. medianb. altitude d. midsegment
____ 56. Name the smallest angle of ∆ABC. The diagram is not to scale.
a. ∠Ab. ∠Cc. Two angles are the same size and smaller than the third.d. ∠B
____ 57. Which three lengths could be the lengths of the sides of a triangle?a. 12 cm, 5 cm, 17 cm c. 9 cm, 22 cm, 11 cmb. 10 cm, 15 cm, 24 cm d. 21 cm, 7 cm, 6 cm
____ 58. ABCD is a parallelogram. If m∠CDA = 66, then m∠BCD = ? . The diagram is not to scale.
a. 66 b. 124 c. 114 d. 132
Name: ________________________ ID: A
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____ 59. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.
a. x = 7, NM = 20, OL = 22 c. x = 7, NM = 22, OL = 22b. x = 5, NM = 20, OL = 20 d. x = 5, NM = 22, OL = 20
____ 60. Find the values of the variables in the parallelogram. The diagram is not to scale.
a. x = 49, y = 29, z = 102 c. x = 49, y = 49, z = 131b. x = 29, y = 49, z = 131 d. x = 29, y = 49, z = 102
____ 61. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.
Given: XY ≅ WZ and XW ≅ YZ
a. No; you cannot determine that the quadrilateral is a parallelogram.b. Yes; two opposite sides are both parallel and congruent.c. Yes; opposite sides are congruent.d. Yes; diagonals of a parallelogram bisect each other.
Name: ________________________ ID: A
17
____ 62. Find the values of a and b.The diagram is not to scale.
a. a = 144, b = 67 c. a = 113, b = 67b. a = 144, b = 36 d. a = 113, b = 36
____ 63. Find m∠1 andm∠3 in the kite. The diagram is not to scale.
a. 51, 51 b. 39, 39 c. 39, 51 d. 51, 39
____ 64. Which description does NOT guarantee that a trapezoid is isoscles?a. congruent diagonals b. both pairs of base angles congruent c. congruent basesd. congruent legs
____ 65. The two rectangles are similar. Which is a correct proportion for corresponding sides?
a.12
8=
x
4b.
12
4=
x
8c.
12
4=
x
20d.
4
12=
x
8
Name: ________________________ ID: A
18
____ 66. ∆QRS ∼ ∆TUV. What is the measure of ∠V?
a. 70° b. 110° c. 250° d. 35°
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
____ 67.
a. ∆ABC ∼ ∆MNO; SSS c. ∆ABC ∼ ∆MNO; AAb. ∆ABC ∼ ∆MNO; SAS d. The triangles are not similar.
____ 68. A triangle has side lengths of 10 cm, 24 cm, and 30 cm. Classify it as acute, obtuse, or right.a. acute b. right c. obtuse
Name: ________________________ ID: A
19
Find the slope of the line.
____ 69.
a. −14
b.14
c. −4 d. 4
Find the slope of the line that passes through the pair of points.
____ 70. (1, 7), (10, 1)
a.32
b. −23
c. −32
d.23
Find the slope and y-intercept of the line.
____ 71. y = 43
x – 3
a. 3; 43
b. –3;43
c.34
; 3 d.43
; –3
____ 72. 14x + 4y = 24
a. −27
; 6 c. −72
; 16
b. −72
; 6 d.72
; −6
Write an equation of a line with the given slope and y-intercept.
____ 73. m = 1, b = 4a. y = 4x + 1 c. y = –1x + 4b. y = x – 4 d. y = x + 4
Name: ________________________ ID: A
20
Write the slope-intercept form of the equation for the line.
____ 74.
a. y = 3x − 1 c. y = 13
x + 1
b. y = −3x − 1 d. y = 13
x − 1
Name: ________________________ ID: A
21
____ 75. Use the slope and y-intercept to graph the equation.
y = 34
x – 3
a. c.
b. d.
Find the x- and y-intercept of the line.
____ 76. 2x + 3y = –18a. x-intercept is 18; y-intercept is 18. c. x-intercept is 2; y-intercept is 3.b. x-intercept is –6; y-intercept is –9. d. x-intercept is –9; y-intercept is –6.
Name: ________________________ ID: A
22
Match the equation with its graph.
____ 77. –7x + 7y = –49a. c.
b. d.
____ 78. Write y = 23
x + 7 in standard form using integers.
a. –2x + 3y = 21 c. –2x – 3y = 21b. 3x – 2y = 21 d. –2x + 3y = 7
Name: ________________________ ID: A
23
Write an equation in point-slope form for the line through the given point with the given slope.
____ 79. (4, –6); m = 35
a. y + 6 = 35
x − 4 c. y + 6 = 35
(x − 4)
b. y − 6 = 35
(x + 4) d. y − 4 = 35
(x + 6)
____ 80. A line passes through (1, –5) and (–3, 7).a. Write an equation for the line in point-slope form.b. Rewrite the equation in slope-intercept form.
a. y – 5 = 3(x + 1); y = 3x + 8 c. y − 5 = 13
(x + 1); y = 13
x + 163
b. y − 1 = 13
(x + 5); y = 13
x + 83
; d. y + 5 = –3(x – 1); y = –3x – 2
Write an equation for the line that is parallel to the given line and that passes through the given point.
____ 81. y = –5x + 3; (–6, 3)a. y = –5x + 27 c. y = 5x – 9b. y = –5x – 27 d. y = –5x + 9
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
____ 82. 7x – 4y = 4x – 4y = 3a. perpendicular b. parallel c. neither
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
____ 83. y = 23
x + 9; (–6, 5)
a. y = −23
x + 1 c. y = 23
x + 9
b. y = −32
x + 32
d. y = −32
x − 4
Name: ________________________ ID: A
24
____ 84. Which statement can you conclude is true from the given information?
Given: AB→←
is the perpendicular bisector of IK .
a. AJ = BJ c. IJ = JK
b. ∠IAJ is a right angle. d. A is the midpoint of IK .
____ 85. Find the length of AB, given that DB is a median of the triangle and AC = 26.
a. 13 c. 52b. 26 d. not enough information
Name: ________________________ ID: A
25
Short Answer
86. State the missing reasons in this proof.
Given: ∠1 ≅ ∠5Prove: p Ä r
Statements Reasons
1.∠1 ≅ ∠5
2.∠4 ≅ ∠1
3.∠4 ≅ ∠5
4.p Ä r
Given
a.____
b.____
c.____
87. Find the measure of each interior and exterior angle. The diagram is not to scale.
88. Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
89. Isosceles trapezoid ABCD has legs AB and CD, and base BC. If AB = 4y – 3, BC = 3y – 4, and CD = 5y – 10, find the value of y.
Name: ________________________ ID: A
26
90. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.
Essay
91. Write a two-column proof.
Given: ∠2 and∠5 are supplementary.Prove: l Ä m
Name: ________________________ ID: A
27
92. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
93. Write a two-column proof.
Given: BC ≅ EC and AC ≅ DC
Prove: BA ≅ ED
Other
94. Give a convincing argument that quadrilateral ABCD with A(–3, –4), B(0, –2), C(6, –2), and D(3, –4) is a parallelogram.
95. In the coordinate plane, draw quadrilateral ABCD with A(–5, 0), B(2, –6), C(8, 1), and D(1, 7).Then demonstrate that ABCD is a rectangle.
ID: A
1
Geo X Midterm Exam Review PacketAnswer Section
MULTIPLE CHOICE
1. ANS: B PTS: 1 DIF: L3 REF: 1-3 Points, Lines, and PlanesOBJ: 1-3.2 Basic Postulates of Geometry NAT: NAEP 2005 G1c | ADP K.1.1TOP: 1-4 Example 4 KEY: point | plane
2. ANS: A PTS: 1 DIF: L2 REF: 1-4 Segments, Rays, Parallel Lines and Planes OBJ: 1-4.1 Identifying Segments and Rays NAT: NAEP 2005 G3gTOP: 1-4 Example 1 KEY: ray
3. ANS: C PTS: 1 DIF: L2 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1TOP: 1-5 Example 1 KEY: segment | segment length
4. ANS: A PTS: 1 DIF: L2 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1TOP: 1-5 Example 2 KEY: segment | segment length
5. ANS: A PTS: 1 DIF: L2 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1TOP: 1-5 Example 3 KEY: segment | segment length | midpoint | multi-part question
6. ANS: C PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.1 Finding Angle Measures NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B TOP: 1-6 Example 3 KEY: Angle Addition Postulate
7. ANS: D PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.1 Finding Angle Measures NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B TOP: 1-6 Example 3 KEY: Angle Addition Postulate
8. ANS: C PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B TOP: 1-6 Example 4 KEY: supplementary angles
9. ANS: D PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B TOP: 1-6 Example 4 KEY: supplementary angles | complementary angles
10. ANS: C PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B TOP: 1-6 Example 4 KEY: complementary angles
11. ANS: D PTS: 1 DIF: L3 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B KEY: complementary angles
12. ANS: B PTS: 1 DIF: L3 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: PA 2.3.B KEY: supplementary angles
13. ANS: C PTS: 1 DIF: L2 REF: 1-7 Basic ConstructionsOBJ: 1-7.2 Constructing Bisectors NAT: NAEP 2005 G3b | ADP K.2.2 | ADP K.2.3STA: PA 2.3.B TOP: 1-7 Example 4 KEY: angle bisector
ID: A
2
14. ANS: D PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.1 Finding Perimeter and Circumference NAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: PA 2.5.A TOP: 1-9 Example 2 KEY: circle | circumference
15. ANS: D PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.2 Finding AreaNAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: PA 2.5.A TOP: 1-9 Example 5 KEY: area | circle
16. ANS: D PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.2 Finding AreaNAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: PA 2.5.A TOP: 1-9 Example 6 KEY: area | rectangle
17. ANS: B PTS: 1 DIF: L3 REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.2 Finding AreaNAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: PA 2.5.A KEY: area | square
18. ANS: D PTS: 1 DIF: L2 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 TOP: 2-4 Example 3KEY: Properties of Equality
19. ANS: A PTS: 1 DIF: L2 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 TOP: 2-4 Example 3KEY: Properties of Congruence
20. ANS: A PTS: 1 DIF: L2 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 TOP: 2-4 Example 3KEY: Properties of Congruence
21. ANS: C PTS: 1 DIF: L3 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 TOP: 2-4 Example 3KEY: Properties of Congruence
22. ANS: A PTS: 1 DIF: L2 REF: 2-5 Proving Angles CongruentOBJ: 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1TOP: 2-5 Example 1 KEY: vertical angles | Vertical Angles Theorem
23. ANS: A PTS: 1 DIF: L2 REF: 2-5 Proving Angles CongruentOBJ: 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1TOP: 2-5 Example 1 KEY: Vertical Angles Theorem | vertical angles
24. ANS: A PTS: 1 DIF: L2 REF: 2-5 Proving Angles CongruentOBJ: 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1TOP: 2-5 Example 1 KEY: Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question
25. ANS: A PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.1 Identifying Angles NAT: NAEP 2005 M1f | ADP K.2.1TOP: 3-1 Example 1 KEY: corresponding angles | transversal | parallel lines
ID: A
3
26. ANS: C PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1TOP: 3-1 Example 4 KEY: parallel lines | alternate interior angles
27. ANS: B PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1TOP: 3-1 Example 5 KEY: corresponding angles | parallel lines |
28. ANS: C PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1KEY: transversal | parallel lines
29. ANS: C PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1KEY: transversal | parallel lines | supplementary angles
30. ANS: A PTS: 1 DIF: L2 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3TOP: 3-2 Example 1 KEY: parallel lines | reasoning
31. ANS: D PTS: 1 DIF: L2 REF: 3-3 Parallel and Perpendicular Lines OBJ: 3-3.1 Relating Parallel and Perpendicular Lines NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1 TOP: 3-3 Example 2KEY: parallel lines
32. ANS: A PTS: 1 DIF: L3 REF: 3-3 Parallel and Perpendicular Lines OBJ: 3-3.1 Relating Parallel and Perpendicular Lines NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1 TOP: 3-3 Example 2KEY: parallel lines | perpendicular lines | transversal
33. ANS: B PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-4 Example 1 KEY: triangle | sum of angles of a triangle
34. ANS: D PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-4 Example 1 KEY: triangle | sum of angles of a triangle
35. ANS: D PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-4 Example 2 KEY: acute triangle | triangle | classifying triangles | scalene | isosceles triangle | equilateral
36. ANS: D PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-4 Example 2 KEY: triangle | classifying triangles | right triangle | obtuse triangle | acute triangle
ID: A
4
37. ANS: A PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.2 Using Exterior Angles of Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-4 Example 3 KEY: triangle | sum of angles of a triangle
38. ANS: B PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: triangle | sum of angles of a triangle | vertical angles
39. ANS: D PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 TOP: 3-5 Example 3 KEY: sum of angles of a polygon
40. ANS: C PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: angle | triangle | exterior angle | Polygon Angle-Sum Theorem
41. ANS: C PTS: 1 DIF: L3 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: sum of angles of a polygon
42. ANS: D PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: Polygon Angle-Sum Theorem
43. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: Polygon Exterior Angle-Sum Theorem
44. ANS: C PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Using the SSS and SAS Postulates NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-2 Example 1 KEY: SSS | reflexive property | proof
45. ANS: B PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-3 Example 1 KEY: ASA
46. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-3 Example 3 KEY: ASA | reasoning
47. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-3 Example 4 KEY: ASA | reasoning
ID: A
5
48. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-3 Example 3 KEY: ASA | AAS | SAS
49. ANS: D PTS: 1 DIF: L2 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: 4-4.1 Proving Parts of Triangles Congruent NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B TOP: 4-4 Example 1 KEY: ASA | CPCTC | proof
50. ANS: A PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems NAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3 TOP: 4-5 Example 2KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
51. ANS: D PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems NAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3 TOP: 4-5 Example 2KEY: isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
52. ANS: C PTS: 1 DIF: L2 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2STA: PA 2.9.D TOP: 5-1 Example 1 KEY: midsegment | Triangle Midsegment Theorem
53. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2KEY: midpoint | midsegment | Triangle Midsegment Theorem
54. ANS: B PTS: 1 DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2TOP: 5-2 Example 2 KEY: angle bisector | Converse of the Angle Bisector Theorem
55. ANS: D PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and AltitudesNAT: NAEP 2005 G3b TOP: 5-3 Example 4 KEY: altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangle
56. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.1 Inequalities Involving Angles of Triangles NAT: NAEP 2005 G3fTOP: 5-5 Example 2 KEY: Theorem 5-10
57. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3fTOP: 5-5 Example 4 KEY: Triangle Inequality Theorem
58. ANS: C PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f TOP: 6-2 Example 1 KEY: parallelogram | consectutive angles
59. ANS: B PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f STA: PA 2.9.C TOP: 6-2 Example 2 KEY: parallelogram | algebra | Theorem 6-1
60. ANS: D PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f STA: PA 2.9.C KEY: parallelogram | opposite angles | consectutive angles | transversal
ID: A
6
61. ANS: C PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral is a Parallelogram OBJ: 6-3.1 Is the Quadrilateral a Parallelogram? NAT: NAEP 2005 G3fSTA: PA 2.9.C TOP: 6-3 Example 2 KEY: parallelogram | opposite sides | Theorem 6-7
62. ANS: A PTS: 1 DIF: L2 REF: 6-5 Trapezoids and KitesOBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3fSTA: PA 2.9.C TOP: 6-5 Example 1 KEY: trapezoid | base angles | Theorem 6-15
63. ANS: C PTS: 1 DIF: L2 REF: 6-5 Trapezoids and KitesOBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3fSTA: PA 2.9.C TOP: 6-5 Example 3 KEY: kite | Theorem 6-17 | diagonal
64. ANS: C PTS: 1 DIF: L4 REF: 6-5 Trapezoids and KitesOBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3fSTA: PA 2.9.C KEY: trapezoid | isosceles trapezoid | reasoning
65. ANS: B PTS: 1 DIF: L2 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: PA 2.9.B TOP: 7-2 Example 1 KEY: similar polygons | corresponding sides
66. ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: PA 2.9.BTOP: 7-3 Example 1 KEY: Angle-Angle Similarity Postulate | corresponding angles
67. ANS: A PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: PA 2.9.BTOP: 7-3 Example 2 KEY: Side-Side-Side Similarity Theorem
68. ANS: C PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.2 The Converse of the Pythagorean Theorem NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3STA: PA 2.10.B TOP: 8-1 Example 5 KEY: right triangle | obtuse triangle | acute triangle
69. ANS: A PTS: 1 DIF: L2 REF: 6-1 Rate of Change and SlopeOBJ: 6-1.2 Finding Slope NAT: NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1STA: PA M11.C.2 | PA M11.D.3 | PA M11.D.3.1.1 | PA M11.D.3.1.2 | PA M11.D.3.2 | PA M11.D.3.2.1TOP: 6-1 Example 3 KEY: graphing | finding slope using a graph | slope
70. ANS: B PTS: 1 DIF: L2 REF: 6-1 Rate of Change and SlopeOBJ: 6-1.2 Finding Slope NAT: NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1STA: PA M11.C.2 | PA M11.D.3 | PA M11.D.3.1.1 | PA M11.D.3.1.2 | PA M11.D.3.2 | PA M11.D.3.2.1TOP: 6-1 Example 4 KEY: finding slope using points | slope
71. ANS: D PTS: 1 DIF: L2 REF: 6-2 Slope-Intercept FormOBJ: 6-2.1 Writing Linear Equations NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.3.2.2 | PA M11.D.3.2.3 TOP: 6-2 Example 1 KEY: linear equation | y-intercept | slope
ID: A
7
72. ANS: B PTS: 1 DIF: L3 REF: 6-2 Slope-Intercept FormOBJ: 6-2.1 Writing Linear Equations NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.3.2.2 | PA M11.D.3.2.3 TOP: 6-2 Example 1 KEY: slope | linear equation | y-intercept
73. ANS: D PTS: 1 DIF: L2 REF: 6-2 Slope-Intercept FormOBJ: 6-2.1 Writing Linear Equations NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.3.2.2 | PA M11.D.3.2.3 TOP: 6-2 Example 2 KEY: linear equation | slope | y-intercept
74. ANS: A PTS: 1 DIF: L2 REF: 6-2 Slope-Intercept FormOBJ: 6-2.1 Writing Linear Equations NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.3.2.2 | PA M11.D.3.2.3 TOP: 6-2 Example 3 KEY: graphing | slope | y-intercept | slope-intercept form | finding slope using a graph
75. ANS: D PTS: 1 DIF: L2 REF: 6-2 Slope-Intercept FormOBJ: 6-2.2 Graphing Linear Equations NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.3.2.2 | PA M11.D.3.2.3 TOP: 6-2 Example 4 KEY: linear equation | graphing equations | slope | y-intercept
76. ANS: D PTS: 1 DIF: L2 REF: 6-4 Standard FormOBJ: 6-4.1 Graphing Equations Using Intercepts NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2 STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-4 Example 1KEY: standard form of a linear equation | x-intercept | y-intercept
77. ANS: A PTS: 1 DIF: L2 REF: 6-4 Standard FormOBJ: 6-4.1 Graphing Equations Using Intercepts NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2 STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-4 Example 2KEY: graphing | x-intercept | y-intercept | standard form of a linear equation
78. ANS: A PTS: 1 DIF: L2 REF: 6-4 Standard FormOBJ: 6-4.2 Writing Equations in Standard Form NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2 STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-4 Example 4KEY: standard form of a linear equation | transforming equations
79. ANS: C PTS: 1 DIF: L2 REF: 6-5 Point-Slope Form and Writing Linear Equations OBJ: 6-5.1 Using Point-Slope FormNAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2 STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-5 Example 2KEY: slope-intercept form | linear equation
80. ANS: D PTS: 1 DIF: L2 REF: 6-5 Point-Slope Form and Writing Linear Equations OBJ: 6-5.1 Using Point-Slope FormNAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2 STA: PA M11.C.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-5 Example 3KEY: point-slope form | slope-intercept form | transforming equations | multi-part question
ID: A
8
81. ANS: B PTS: 1 DIF: L2 REF: 6-6 Parallel and Perpendicular Lines OBJ: 6-6.1 Parallel LinesNAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2STA: PA M11.C.2 | PA M11.C.2.1.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-6 Example 2 KEY: parallel lines | linear equation
82. ANS: C PTS: 1 DIF: L3 REF: 6-6 Parallel and Perpendicular Lines OBJ: 6-6.2 Perpendicular LinesNAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2STA: PA M11.C.2 | PA M11.C.2.1.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-6 Example 3 KEY: perpendicular lines | parallel lines
83. ANS: D PTS: 1 DIF: L2 REF: 6-6 Parallel and Perpendicular Lines OBJ: 6-6.2 Perpendicular LinesNAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2STA: PA M11.C.2 | PA M11.C.2.1.2 | PA M11.D.2.1 | PA M11.D.2.1.3 TOP: 6-6 Example 3 KEY: perpendicular lines | linear equation
84. ANS: C PTS: 1 DIF: L3 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2KEY: perpendicular bisector | Perpendicular Bisector Theorem | reasoning
85. ANS: A PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and AltitudesNAT: NAEP 2005 G3b TOP: 5-3 Example 3 KEY: median of a triangle
SHORT ANSWER
86. ANS: a. Vertical angles.b. Transitive Property.c. Alternate Interior Angles Converse.
PTS: 1 DIF: L2 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3TOP: 3-2 Example 1 KEY: two-column proof | proof | reasoning | corresponding angles | multi-part question
87. ANS: m∠1 = m∠2 = m∠3 = 90,m∠4 = 122,m∠5 = m∠6 = 58,m∠8 = 32,m∠7 = m∠9 = 148
PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum TheoremOBJ: 3-4.2 Using Exterior Angles of Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: Triangle Angle-Sum Theorem | exterior angle
ID: A
9
88. ANS: m∠(interior) = 120m∠(exterior) = 60
PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum TheoremsOBJ: 3-5.2 Polygon Angle Sums NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: Polygon Exterior Angle-Sum Theorem | exterior angle | interior angle
89. ANS: 7
PTS: 1 DIF: L2 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals NAT: NAEP 2005 G3fKEY: isosceles trapezoid | algebra
90. ANS: Rhombus; the measure of all numbered angles equal 39.
PTS: 1 DIF: L2 REF: 6-4 Special ParallelogramsOBJ: 6-4.1 Diagonals of Rhombuses and Rectangles NAT: NAEP 2005 G3fSTA: PA 2.9.C KEY: parallelogram | rhombus | reasoning
ESSAY
91. ANS: [4] Statements Reasons
1. ∠2 and∠5 are supplementary
2. ∠3 ≅ ∠2
3. ∠3 and∠5 are supplementary
4. l Ä m
1. Given
2. Vertical angles
3. Substitution
4. Converse of Same-SideInterior Angles Theorem
[3] correct idea, some details inaccurate[2] correct idea, some statements missing[1] correct idea, several steps omitted
PTS: 1 DIF: L4 REF: 3-2 Proving Lines ParallelOBJ: 3-2.1 Using a Transversal NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3KEY: two-column proof | proof | extended response | rubric-based question | parallel lines | supplementary angles
ID: A
10
92. ANS: [4] w + 31 + 90 = 180, so w = 59º. Since vertical angles are congruent, y = 59º. Since
supplementary angles have measures with sum 180, x = v = 121º. z + 68 + y = z + 68 + 59 = 180, so z = 53º.
[3] small error leading to one incorrect answer[2] three correct answers, work shown[1] two correct answers, work shown
PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum TheoremOBJ: 3-4.2 Using Exterior Angles of Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 KEY: Triangle Angle-Sum Theorem | vertical angles | supplementary angles | extended response | rubric-based question
93. ANS: [4]
Statement Reason
1. BC ≅ EC and AC ≅ DC 1. Given
2. ∠BCA ≅ ∠ECD 2. Vertical angles are congruent.3. ∆BCA ≅ ∆ECD 3. SAS
4. BA ≅ ED 4. CPCTC
[3] correct idea, some details inaccurate[2] correct idea, not well organized[1] correct idea, one or more significant steps omitted
PTS: 1 DIF: L4 REF: 4-4 Using Congruent Triangles: CPCTCOBJ: 4-4.1 Proving Parts of Triangles Congruent NAT: NAEP 2005 G2e | ADP K.3STA: PA 2.9.B KEY: CPCTC | congruent figures | proof | SAS | rubric-based question | extended response
OTHER
94. ANS:
Slope of AB is 23
.
Slope of CD is 23
.
Slope of BC is 0.
Slope of AD is 0.
AB Ä CD and BC Ä AD.Therefore ABCD is a parallelogram.
PTS: 1 DIF: L3 REF: 6-3 Proving That a Quadrilateral is a ParallelogramOBJ: 6-3.1 Is the Quadrilateral a Parallelogram? NAT: NAEP 2005 G3fSTA: PA 2.9.C KEY: parallelogram | coordinate plane | algebra | slope | writing in math
ID: A
11
95. ANS:
Answers may vary. Sample:
slope of AB is −67
slope of BC is 76
slope of CD is −67
slope of AD is 76
AB Ä CD andBC Ä AD , so ABCD is a parallelogram.
AB ⊥ BC, BC ⊥ CD, CD ⊥ AD, and AB ⊥ AD.∠ABC, ∠BCD,∠CDA, ∠BAD are right angles.ABCD is a rectangle.
PTS: 1 DIF: L4 REF: 6-7 Proofs Using Coordinate GeometryOBJ: 6-7.1 Building Proofs in the Coordinate Plane NAT: NAEP 2005 G4dSTA: PA 2.9.G | PA 2.5.B | PA 2.8.J KEY: coordinate plane | proof | reasoning | rectangle | slope | multi-part question
ID: A Geo X Midterm Exam Review Packet [Answer Strip]
_____ 1.B
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ID: A Geo X Midterm Exam Review Packet [Answer Strip]
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ID: A Geo X Midterm Exam Review Packet [Answer Strip]
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ID: A Geo X Midterm Exam Review Packet [Answer Strip]
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ID: A Geo X Midterm Exam Review Packet [Answer Strip]
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