Geometry CP – Semester 1 Review Packet Name:______________________________

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Additional Notes:

Geometry CP - Semester 1 Review Name: ______________________

1. Predict the next number. a. 1, 3, 7, 13, … _____ b. 500, 100, 20, 4, … _____

2. In the diagram of collinear points, 3. Suppose J is between H and K. (draw a diagram)

AB = BC = CD, AC = 10, and BE = 32. HJ = 4x – 7, JK = 2x – 3, and HK = 68.

x = _____

AB = _____ HJ = _____

DE = _____ JK = _____

Is J the midpoint? _____

4. Find the distance, slope, and midpoint between the points. a. (-3, 7) and (7, 11) b. (-1, -4) and (3, -9)

distance = _____ distance = _____

midpoint = _____ midpoint = _____

slope = _____ slope = _____

5. If mDBC = 72, 6. mABD = (4x - 1)

find mABD mDBC = (3x + 5)

mABC = 81

x = _______

mABD = _______

mDBC = _______

7. mCBD = 35

mABC = 113 List all the acceptable names for the angle

mABD = _____ marked with one arc.

8. PT is an angle bisector of RPS.

a. mTPS = 39 b. mRPT = (6x - 17)

mRPT = _____ mTPS = (x + 28)

mRPS = _____ x = _____

mRPS = _____

9. Use diagram below for each. . a. m2 = 132 b. m1 = (4x - 3)

m3 = _____ m4 = (5x - 6)

m4 = _____ x = _____

m3 = _____

c. m1 = (3x + 32) d. m1 = (10x - 51)

m3 = (5x - 12) m2 = (2y)

x = _____ m3 = (6x - 11)

m1 = _____ x = _____

y = _____

10. Find the perimeter and area of each figure.

a. b.

Perimeter = __________ Perimeter = __________

Area = __________ Area = __________

11. If the area of a rectangle is 84 square feet and the height is 7 feet, find the base.

12. If the area of a triangle is 48 square yards and the base is 6 yards, find the height.

13. If 4 and 5 are supplementary and m4 = 19, find m5.

14. The midpoint of a segment is (-10, -16). One endpoint is (1, -8). Find the other endpoint.

15. Two angles are complementary, and one angle has a measure that is 9 times the measure of the

other angle. What is the measure of the larger angle?

16. Use the diagram at the right.

a. If mAFB = 68o, what is the m EFG?

b. If mAFB = 68o, what is the mAFE?

c. If GED is complementary to DEH

and mGED = 46o; what is the mDEH?

d. If FGC is supplementary to AFB and

mAFB = 68o; what is the m FGC?

e. If m EFG = 68o, EFG FGE, and

FGE GDE + 44o; what is the mGDE?

f. If FEG is complementary to GED and

GED is complementary to DEH, what

is m FEG if mDEH = 44o?

g. If mCGD = 68o and CGF BFG, what

is mAFB?

17. Write the equation of a line that passes through (5, -7) and is parallel to y = -5x + 2.

18. Find the equation of a line that passes through (5, -7) and is perpendicular to y = -5x + 2.

19. If AB CD , find x and y. 20. If AB CD and m 1 = 68o, find m 4.

21. Find the values of the variables in each diagram.

a.

b.

c.

d.

e.

f.

g.

h.

22. Find the value of x that makes AB ||CD . a. b.

23. Supply the conclusion with a reason for each diagram and set of givens.

a) GIVEN Conclusion Reason

1 and 2 are supp.

3 and 1 are supp.

b) GIVEN Conclusion Reason

m // n

c) GIVEN Conclusion Reason

7 8

d) GIVEN Conclusion Reason

RS SE

e) GIVEN Conclusion Reason

Diagram as shown

24. Rewrite the conditional statement in if-then form.

a. Supplementary angles have a sum of 180o.

b. Freshmen and sophomores are not allowed to drive to school.

25. Identify the hypothesis and the conclusion of each statement.

a. Skew lines lie in different planes. b. I’ll go to the game, if I don’t have to work.

hypothesis: hypothesis:

conclusion: conclusion

c. What is the negation of “It is sunny” ?

26. Rewrite “Vertical angles are congruent” in conditional form and its converse.

Conditional:

Converse:

Is the statement biconditional? If so, write in biconditional form. If not, give a counterexample.

27. Write a conclusion using the true statements. If no conclusion is possible, write no conclusion.

If Al eats an apple, then Betty will buy a basketball.

If Betty buys a basketball, the Charlie will eat cake.

If Charlie eats cake, then Ditka will drive in the Daytona 500.

Al is eating an Apple.

Conclusion (if any):

28. Determine if the conclusion makes sense.

If you practice, then you will remember all the lines.

If you remember all the lines, you will get selected to be in the show.

You got selected for the show; therefore you went to practice.

True or False. Reasoning:

29. Use the given to determine which statements are true:

Given:a // b Statements: a) 1 8

b) 1 is supp. to 3

c) 5 7

d) 6 is supp. to 7

e) 2 3

f) if t b, then b a

g) 5 8

h) 3 and 7 are complementary

30. Classify the triangles by angles and by sides.

a) b) c)

angles: ________ angles: ________ angles: ________

sides: ________ sides: ________ sides: ________

31. Find the value of x.

a) b)

32. Solve to find the variables.

a) b) c)

d) e) f)

33. In ABC , mA = 54o. The m B is 6 times the mC. Find the measure of each angle.

(Draw a diagram)

34. In BFG , m F = 87o. The m B is 7 times mG. Find the measure of each angle.

(Draw a diagram)

35. In ABC , find x, and the measures of angles A, B and C. Also, classify ABC by its angles if

mA = (5x – 10)⁰, m B = (4x-30)⁰, mC = 67⁰. (Draw a diagram.)

36. ABC DEF . Solve to find x and y.

a) b) The perimeter of ∆ABC is 41.

37. In the triangle, mC = 60° and mV = 59°.

Name the shortest side and the longest side.

shortest side:

longest side:

38. Given: KP is the bisector of RQ

KP bisects RKQ

LM = 18

NQ = 15,

RP = 12

Find QR and MN. QR = ________

MN = ________

39. The lengths of two sides of a triangle are given to be 21 meters and 17 meters long. Describe the

possible lengths of the third side.

40. The measures of two sides of a triangle are given to be 9 feet and 10 feet long. Find a length of a

segment whose measure would be too long to form a triangle with the given two measures.

41. Given: PW = 30, KD = 70, AD = 80. 42. Fill each blank with <, >, or =.

find the perimeter of ΔHPW.

a. AF _____ DL

b. WGP _____ HGP

43. Write an inequality that compares QD to QZ.

Then solve the inequality for x.(Not drawn to scale.)

44. Write an inequality using the Hinge Theorem 45. In the diagram,HC is an angle bisector of

(or converse) describing the restriction on x. ΔDHL. Solve for x and find DL.

Then, solve it for x.

46. In the figure, TM is an altitude of ΔATJ . 47. Determine whether GR is a median of

Find the value of x and AT. ΔNRP. Show work to justify your answer.

48. Given: AC is an altitude of ΔABE 49. Find the coordinates of the endpoints of the

ΔABD is equilateral of the midsegment parallel to AC .

AD is a median of ΔABE AB = 32

Find CE and m ADE.

50. Find the value of x and list the sides of ΔABC in order from shortest to longest if:

9 29m A x

93 5m B x

10 2m C x

(Draw a diagram.) x = __________

order of sides = __________

51. Given the diagram as marked. Find x and KM. 52. F, G, and E are midpoints of the sides of ΔBMY. If FG = 2x – 1 and BY = 5x – 7, find BE and BY.

53. Determine if each pair of triangles can be proved to be congruent. If so, state the reason.

a) b) c)

d) e) f)

MD is a median MD is an altitude

54. What does CPCTC stand for and when is it used?

55. Give the name of any quadrilateral with the following characteristics:

a) both pairs of opposite sides parallel

b) one pair of opposite sides parallel

c) opposite sides congruent

d) opposite angles congruent

e) all right angles

f) all sides congruent

d) Quadrilateral with all sides congruent and right angles.

56. List 5 properties of PARALLELOGRAMS

1.

2.

3.

4.

5.

57. Find the value of each variable in the parallelogram. 57c. Find mE. (not a parallelogram)

a) b) c)

58. Find the missing lengths of the parallelogram: 59. Find the value of x that makes the

JK = _____ polygon a parallelogram.

JM = _____

MK = _____

JL = _____

60. Find the value(s) of x that will make the polygon a parallelogram.

a) b)

61. Find the value of each variable and the missing lengths in the parallelogram.

a) b)

x = _______ x = _______

HK _______ y = _______

Part 2. Proofs. You will need extra paper to complete most of the proofs.

1. Use coordinate geometry to verify LUKE

is a parallelogram. Show all work and

state the reason that proves the shape

is a parallelogram.

How do you know it is NOT a rectangle

based on coordinate geometry?

2. Given: Wis a right angle 3. Given: O is the midpoint ofDG

S is a right angle Prove: DO OG Prove: W S

4. Given: 2 3 5. Given: RS ST

Prove: m // n WT ST

Prove: S T

6. Given: 2 3 7. Given: 5 8

Prove: 1 4 Prove: 1 4

8. Given: BC EF 9. Given: C is the midpoint of BD

BA ED AB // DE

B E Prove: AB ED

Prove: ABC DEF

10. Given: ID is an altitude of isosceles ΔVKI

Prove: DV DK

Statements Reasons

1. ID is an alt. of isos. ΔVKI 1.

2. IDV and IDK are rt. ’s 2.

3. IDV IDK 3.

4. ID ID 4.

5. V K 5.

6. VDI KDI 6.

7. 7.

11. Use slope to determine which lines are perpendicular. Justify your reason.

1. a. 21 2. AB = 5 3. x = 13 4a. d =2 29 b. d = 41

b. 4/5 DE = 22 HJ = 45 mid = (2,9) mid = (1,-6.5) JK = 23 m = 2/5 m = -5/4

5. 18⁰ 6. x = 11 7. mABD= 78⁰ 8a. mRPT = 39⁰ b. x = 9 mABD= 43⁰ mRPS = 78⁰ mRPS = 74⁰ mDBC= 38⁰, the angle can be named ABD or DBA

9a. m3 = 48⁰ b. x = 21 c. x = 22 d. x = 10 10a. P = 28 b. P = 38 m4 =132 m3 =81 m1 =98 y = 65.5 A = 40 A = 42.5

11. 12 16a. 68⁰ 17. y = -5x + 18 21a.x= 110⁰ y = 110⁰ 22a. 56 12. 16 b. 112⁰ b. x = 115⁰ y = 115 22b. 74 13. 161⁰ c. 44⁰ 18. y = 1/5x – 8 c. x = 90⁰ y = 90⁰ 14. (-21,-24) d. 112⁰ d. x = 73⁰ y = 41⁰ 15. 81⁰ e. 24⁰ 19. x = 9, y = 54 e. x = 60⁰ y = 60⁰ f. 44⁰ f. x = 50⁰ y = 50⁰ g. 68⁰ 20. m4 = 22⁰ g. x = 45 h. x = 28.5 23. Conclusion Reason

a. 1 3 If ‘s are supp to the same ,→ they are to each other. b. 5 supp 6 If // lines → same side (consecutive) interior ’s are supplementary c. m // n If corresponding ’s are → // lines d. S is the midpoint of RE If a point divides a segment into 2 segments → it is a midpoint or S bisects RE If a point divides a segment into 2 segments → it is bisected e. 1 4 or If ’s are vertical ’s →

1 and 3 are a linear pair If ’s are adjacent and supplementary → linear pair (assumed from diagram)

24a. If ’s are supplementary angles, then they have a sum of 180o. b. If a student is a freshmen or a sophomore, then they are not allowed to drive to school.

25a. h: skew lines b. h: I don’t have to work 26. If angles are vertical angles, then they are congruent. c: lie in different planes c: I’ll go to the game If angles are congruent, then they are vertical angles. Negation: It is not sunny. Not biconditional because the converse is not true.

27. Ditka will drive in the Daytona 500. 30. a. right scalene 31a.70o 28. False. You may be the only person that tried out. b. obtuse isosceles b. x = 7 29. a, c, and d are true (rest are false) c. equilateral equiangular

32a. x = 76⁰ b. x = 8 or -5 c. x = 48⁰ d. x = 15 e. x = 16.4 f. x = 17 y= 23⁰, z = 132⁰ y = 84⁰ y = 40/3 y = 122⁰

33. m A = 54o 34. x = 11.625 35. x = 17 36a. x = 23.7 b. x = 9 37. short = LC

m B = 108⁰ m F = 87⁰ m A = 75⁰ y = 17.8 y = 1 long = VC

m C = 18⁰ m B = 81.375⁰ m B = 38⁰

m G = 11.625⁰ acute scalene

38. QR = 24 39. 4 < x < 38 40. x > 19 41. 105 42a. > b. > 43. 8x – 5 > 7x + 2 MN = 18 x > 7

44. 3x – 3 > 21 45. x = 15 46. x = 8 47. NG = 47 and PG = 73 , not =, so RG is not a median.

x > 8 DL = 92 AT = 135

48. CE = 48 49. (-1,6) & (3,-1) 50. x = 4 51. x = 16 52. x = 5, BE = 9, BY = 18 mADE = 120⁰ AB, BC, AC KM = 184

53a. none 54. Corresponding 55a. parallelogram, rhombus, rectangle, square 56. opp. sides // b. SAS Parts of b. trapezoid, isosceles trapezoid opp. sides c. ASA Congruent c. parallelogram, rhombus, rectangle, square opp. ‘s d. ASA or AAS Triangles are d. parallelogram, rhombus, rectangle, square consecutive ‘ s supp. e. SAS Congruent e. rectangle, square diagonals bisect each f. HL f. square, rhombus other g. square 57a. m = 133⁰ 58. JK =80 59. x = 20.3 60a. x = 4 or 1 61a. x = 7.5 61b. x = 16 n = 47⁰ JM = 52 60b. x = 2 or 5/4 HK = 29 y = -8 t = 78 MK = 62 b.x = 25, y = 24 c. 72o JL = 90

1. Slope of LU and EK = 0/10. Same slope = parallel. Slope of LE and UK = -10/1. Same slope = parallel. However, slopes not opposite reciprocal, so not . Therefore, not a rectangle. 2. 1) W is a right angle 1) Given 2) S is a right angle 2) Given

3) W S 3) If 2 ’s are rt ’s → they are 3. 1) O is the midpt of DG 1) Given

2) DO OG 2) If a pt. is a midpt. → it splits a segment into 2 segments

4. 1) 2 3 1) Given

2) m // n 2) If alternate interior ’s are → parallel lines

5. 1) RS ST 1) Given

2) WT ST 2) Given

3) S is a rt 3) if lines → rt ’s

4) T is a rt 4) same as 3 5) S T 5) if ’s are rt ’s →

6. 1) 2 3 1) Given

2) 1 2 2) If ’s are vertical ’s → 3) 3 4 3) same as 2

4) 1 4 4) transitive (if 2 ’s are to ’s → they are to each other) 7. 1) 5 8 1) Given

2) 5 is supp to 1 2) If 2 ’s form a linear pair → supp 3) 8 is supp to 4 3) same as 2

4) 1 4 4) Supplements of ’s are 8. 1) BC EF 1) Given 2) BA ED 2) Given 3) B E 3) Given

4) ABC DEF 4) SAS

9. 1) C is the midpt of BD 1) Given 2) BC CD 2) If a point is a midpoint → it splits a segment into 2 segments 3) AB // ED 3) Given 4) A E 4) If // lines → alternate interior angles 5) B D 5) same as 4

6) ABC EDC 6) AAS 7) AB ED 7) CPCTC 10. Reasons 1. Given 2. If a segment is an altitude then it forms right angles 3. If right angles, then congruent 4. Reflexive 5. If a triangle is isosceles, then the base angles are congruent 6. AAS 7. CPCTC *The missing statement for #7 is DV DK 11. Slope of AY = 8/3, slope of BD = 4/1, and slope of AB is -1/4, therefore BD AB because they have slopes that are opposite and reciprocal.