Name _______________________ Date _______________ Review ~ Pre AP Geometry Midterm 2019-2020

Vocabulary is on the test, you need to know all, so if you see one you don’t remember or think you need review on, especially formulas, postulates or theorems we haven’t seen in a while, please make sure to review the concept. Vocabulary: Chapters 1, 2, 3, 4, 5, 6 Undefined terms Point Line Plane Collinear Coplanar Noncollinear Noncoplanar Segment Endpoint Ray Opposite rays Postulate Distance formula Congruent Midpoint (definition and formula) Bisect Segment bisector Segment addition postulate Angle addition postulate Angle Vertex Acute angle / triangle

Right angle / triangle Obtuse angle / triangle Straight angle Angle bisector Adjacent angles Linear pair Complementary angles Supplementary angles Vertical angles Inductive reasoning Deductive reasoning Conditional statement Converse Inverse Contrapositive Hypothesis Conclusion Law of detachment Law of syllogism Biconditional statement Postulate Theorem Counterexample Algebraic properties from ch2

Proof Two column proof Parallel lines (and it’s slope) Perpendicular lines (slope) Skew lines Transversal Corresponding angles Alternate interior angles Alternate exterior angles Same side interior angles Slope (formula) Coinciding lines Point slope form Slope intercept form Vertical lines (equation and it’s slope) Horizontal lines (equation and it’s slope) Equiangular triangle Equilateral triangle Scalene triangle Isosceles triangle Triangle sum theorem Exterior angle theorem

Third angles theorem CPCTC SSS SAS ASA AAS HL Included side / angle Isosceles triangle properties/theorems Perpendicular bisectors Angle bisectors Medians Altitudes Circumcenter Incenter Centroid Orthocenter Triangle midsegment theorem Equidistant Point of concurrency Triangle inequality theorem Hinge theorem and it’s converse

1. What are the building blocks of geometry?

_____________________________________________

2. Who is the known as the father of geometry?

___________________________________________

Refer to the figure below to name each of the following. Use appropriate symbols where necessary.

3.__________ The intersection of plane M and L.

4.__________ A ray opposite 𝐷𝐵⃗⃗⃗⃗⃗⃗ .

5.__________ A plane containing 𝐶𝐸⃡⃗ ⃗⃗ .

6.__________ The intersection of L and 𝐶𝐸⃡⃗ ⃗⃗ .

7. _________ Three collinear points

8. _________ Three coplanar points

____ 9. D is between C and E. = , = , and DE = 30. Find CE.

____ 10. Point M is the midpoint of . Find BM.

C D E6 x + 15 30

8x

A BM

4x + 13 3x + 17

M

L

A

B C

D

E

______ 11. B is between A and C. AC = 24 and BC = 11. Find AB. ______ 12. In the diagram, . Find .

______ 13. ∠BDC and ∠CDA form a linear pair. Find m∠BDC.

_____ 14. Find the measures of two complementary angles, A & B.

If mA = (7x + 4) and mB = (4x + 9). _____ 15. Find the midpoint and distance of the segment with the given endpoints. (-7, 7) and (-9, 8)

_____ 16. The complement of a 35 angle is an angle with a measure of:

_____ 17. The supplement of a 25 angle is an angle with a measure of:

_______18. bisects and

Solve for x and find The diagram is not to scale. Use the diagram on the right: 19. Name the type of angles: ______________________ 20. Solve for x: ___________________

D A

B

C

(7x + 34)°

(9x + 46)°

126°

3y°

3x – 6°

Drawing not to scale

Complete the statements:

_______21. and _____ are vertical angles.

_______22. Identify the linear pair(s) that include .

_______23. Identify the adjacent angles that include 9. 24. Find the values of x and y. 25. Find the missing elements in the sequence.

2, 5, 10, 17, 26, 37 65, 82 122, . . . 26. Conditionals are known as ______________________________________. 27. What is a conjecture? _____________________________________ 28. Inductive reasoning is based on __________________________ and deductive reasoning is

__________________________________________________. 29. A counterexample invalidates a statement. TRUE FALSE 30. Write the negation of: Points on the same plane are coplanar. ___________________________________________________________________ 31. When a conditional and its converse are true you can combine them as a ____________________.

Write a conditional statement for the situation described, and then write its converse, inverse, and contrapositive.

Parallel lines do not intersect.

Write the conditional, and then underline the hypothesis once, and the conclusion twice. 32. Conditional:

33. Converse:

34. Inverse:

35. Contrapositive:

If possible, write the biconditional statement, if not tell why. 36. Every isosceles triangle has two congruent sides.

, , , ,

1

2

3

45

6

7 8

9

10

11

12

13

1 32

4

5 6

8 7

9 10

12 11l

mn 37. Identify the transversal and classify the angle pair:

4 and 5_____________________

1 and 7_____________________

12 and 8____________________ Name the indicated angles

38. 4 and 5____________________________

39. 2 and 3____________________________

40. 1 and 7____________________________

41. 6 and 8____________________________

42. 1 and 5____________________________

43. 2 and 6____________________________ 44. If j⫽k , then find the value of x. 45. If p//q , then find the value of x.

46. Find the values of x and y. 47. Find the values of x and y.

Determine whether and are parallel, perpendicular, or neither.

48.

Write equations for the line that are parallel and perpendicular to the given line and that passes through the given point.

49. y = 1

2x – 6; (–12, –18)

1

2

3 4 5

6

7 8

73°

54°(x – 3)° (y – 1)°

50. Are the lines for each pair of equations are parallel, perpendicular, or neither. 3x + 5y = 6 5x – 3y = 2 51. Find the m ∠KMN = ________ 52. Solve for x:

53. x=______ 54. Find m∠A = ______ y=______ z=______ 55. Find the perimeter of the triangle: 56. Find the measures of the acute angles:

57. Use the diagram to finish the congruence statements for the triangles.

△PQR ≅ △_______

△RPQ ≅ △ _________

Q ≅ _________

𝑈𝑉̅̅ ̅̅ ≅ ________

58. Name the corresponding parts that need to be congruent in order to prove that ∆FIG ∆TOM

by AAS: ___________ by ASA: _________ by SAS: _______

E

C

A

D

FB

59. These triangles are congruent by: _______ 60. These triangles are congruent by: _______

61. These triangles are congruent by: _______ 62. These triangles are congruent by: _______ 63.In the diagram, △RST ≅ △XYZ. Find the values of x and y.

64. Points B, D, and F are midpoints of the sides of 65. Name an altitude in the △. ________ EC = 39 and DF = 17. Find AC. The diagram is not to scale. Name a median in the △. ________

66. Find BD. 67. Find m∠BAC.

Z

Y

X

C

B A

A

B

D

C

(7x - 10)°

(2x + 5)°

A

B C9x - 6 7x + 6D

36 36

68. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need?

69. In , N is the incenter, , 70. Graph the equations. and . Find NE. y = 5 and x = -3

71. Write an equation of the perpendicular bisector of the segment with endpoints P(-2, 3) and Q(4, 1) .

A B

C

G

H

25 ft

K

24 ft27 ft

A

B

CN

D

E

F

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

1

2

18

17

Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.

__ 72. 3, 9, 10 73. 40, 9, 41 74. 4, 8, 14

75. List the sides in order from shortest to longest. The diagram is not to scale.

76. Complete the statement with <, >, or =. 77. Find the range of values for x: _____˂ x ˂ _____

78. Simplify the radical: 79. Find the measure of 1

−4√160 = ________

√180 = ________ 80. Identify the constructions shown:

A

B

C

104°39°

37°

81-83 Reflect the figure with the given vertices across the given line.

81. A(-2, 2), B(3, 3), C(2, 1); x-axis 82. P(2, 3), Q(4, 0), R(1, -4), S(0, -2); y-axis

83. F(-5, 0), B(-5, 4), X(-2, 2), P(-4, -2); y = x. Is the dotted line a line of symmetry? Circle YES or NO.

84. YES or NO

85. YES or NO

86-87 Rotate the figure with the given vertices about the origin using the given angle of rotation.

86. P(4, -3), Q(2, -3), R(1, -2), S(3, 0); 180 87. A(4, 4), B(2, 1), C(0, 3); 90

A(___, ___) →A’ (___, ___)

B(___, ___) →B’ (___, ___)

C(___, ___) →C’ (___, ___)

P(___, ___) →P’ (___, ___)

Q(___, ___) →Q’ (___, ___)

R(___, ___) →R’ (___, ___)

S(___, ___) →S’ (___, ___)

F(___, ___) →F’ (___, ___)

B(___, ___) →B’ (___, ___)

X(___, ___) →X’ (___, ___)

P(___, ___) →P’ (___, ___)

P(___, ___) →P’ (___, ___)

Q(___, ___) →Q’ (___, ___)

R(___, ___) →R’ (___, ___)

S(___, ___) →S’ (___, ___)

A(___, ___) →A’ (___, ___)

B(___, ___) →B’ (___, ___)

C(___, ___) →C’ (___, ___)

1 2

3 4

5 6

7 8

q

p

r

88-89 Translate the figure with the given vertices along the given vector. For each vertex, find the new coordinates by adding the horizontal and vertical components of the vector to the old coordinates.

Vectors: (x, y) → (x + a, y + b)

88. D(2, 4), E(4, 1), F(4,-2); -2, -2 89. J(-3, -1), K(-2, -3), L(1, -3),M(2, -1); 3, 4

**Complete the given proofs:

1. Given: 44 – 2(3x + 4) = -18

Prove: x = 9

Statements Reasons

2.

Given:

Prove: ∠1 ≅ ∠8

Statements Reasons

D(___, ___) →D’ (___, ___)

E(___, ___) →E’ (___, ___)

F(___, ___) →F’ (___, ___)

J(___, ___) →J’ (___, ___)

K(___, ___) →K’ (___, ___)

L(___, ___) →L’ (___, ___)

M(___, ___) →M’ (___, ___)

3. Given: G is the midpoint of 𝐹𝐻̅̅ ̅̅ . 𝐸𝐹̅̅ ̅̅ ≅ 𝐸𝐻̅̅ ̅̅

Prove: 1 2

Proof:

Statements Reasons

4. Given: l ǁ n

Prove: 4 ≅ 6

Statements Reasons

5. Given: and

Prove:

Statements Reasons

Q

TP

S

R

6. Given: AX ⊥ BC, X is the midpoint of BC

Prove: ABX ACX

Statements Reasons

7. Given: ABC is isosceles, with base AC, 𝐵𝐷 ̅̅ ̅̅ ̅⊥ 𝐴𝐶̅̅ ̅̅

Prove: AEC is isosceles Proof:

Statements Reasons

ABC is isosceles, with base AC Given

𝐵𝐷̅̅ ̅̅ ⊥ 𝐴𝐶̅̅ ̅̅ Given

B X

A

C

3 4

1 2