Sheets - Mr. Thomas

Math 2201
Chapter 2
Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which pairs of angles are equal in this diagram?
a.
b.
c.
d.
____
a = e, b = d, and c = g
a = e, c = g, and b = f
a = c, e = g, and f = h
a = b, c = d, and e = f
2. In which diagram(s) is AB parallel to CD?
1.
a.
b.
c.
d.
____
Choice 1 only
Choice 2 only
Choice 1 and Choice 2
Neither Choice 1 nor Choice 2
3. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
____
2.
∠d + ∠b = 124°
∠a + ∠c = 180°
180° – ∠f = 118°
∠e + ∠d = 180°
4. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
∠d = ∠b
∠a = ∠e
∠b = ∠f
∠c = ∠e
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Math 2201
____
∠d + ∠g = 180°
∠b + ∠d = 180°
∠f + ∠c = 180°
∠e + ∠a = 180°
7. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
____
∠e = ∠f
∠f = ∠a
∠a = ∠b
∠d = ∠c
6. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
____
Review
5. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
____
Chapter 2
∠a = 36°
∠c = 36°
∠g = 36°
∠d = 36°
8. Which angle property proves ∠PYD = 90°?
a.
b.
c.
d.
corresponding angles
alternate interior angles
alternate exterior angles
supplementary angles
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Math 2201
____
Chapter 2
Review
9. Which angle property proves ∠DAB = 120°?
a.
b.
c.
d.
alternate exterior angles
corresponding angles
vertically opposite angles
alternate interior angles
____ 10. Which angle property proves ∠BEF = 107°?
a.
b.
c.
d.
supplementary angles
alternate exterior angles
alternate interior angles
corresponding angles
____ 11. In which diagrams are two lines parallel?
1.
a.
b.
c.
d.
2.
3.
Choice 1 only
Choice 1 and Choice 3
Choices 1, 2, and 3
Choice 2 and Choice 3
____ 12. Which are the correct measures of the indicated angles?
a.
b.
c.
d.
∠w = 77°, ∠x =103°, ∠y = 103°
∠w = 77°, ∠x =77°, ∠y = 103°
∠w = 103°, ∠x =103°, ∠y = 77°
∠w = 103°, ∠x =77°, ∠y = 77°
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Math 2201
Chapter 2
Review
____ 13. Which are the correct measures for ∠YXZ and ∠XZY?
a.
b.
c.
d.
∠YXZ = 62°, ∠XZY = 87°
∠YXZ = 52°, ∠XZY = 87°
∠YXZ = 52°, ∠XZY = 77°
∠YXZ = 62°, ∠XZY = 77°
____ 14. Which are the correct measures for ∠DCE and ∠CAB?
a. ∠DCE = 31°, ∠CAB = 134°
b. ∠DCE = 47°, ∠CAB = 109°
c. ∠DCE = 13°, ∠CAB = 143°
d. ∠DCE = 37°, ∠CAB = 119°
____ 15. Which are the correct measures for ∠WXZ, ∠UZY, and ∠VYX?
a.
b.
c.
d.
∠WXZ = 157°, ∠UZY = 118°, and ∠VYX = 95°
∠WXZ = 147°, ∠UZY = 108°, and ∠VYX = 85°
∠WXZ = 147°, ∠UZY = 118°, and ∠VYX = 95°
∠WXZ = 157°, ∠UZY = 108°, and ∠VYX = 85°
____ 16. Determine the sum of the measures of the interior angles of this polygon.
a.
b.
c.
d.
720°
1080°
540°
1440°
____ 17. Determine the sum of the measures of the angles in a 12-sided convex polygon.
a.
b.
c.
d.
1080°
3600°
2160°
1800°
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Math 2201
Chapter 2
Review
____ 18. Each interior angle of a regular convex polygon measures 144°.
How many sides does the polygon have?
a.
b.
c.
d.
8
11
9
10
____ 19. Determine the value of a.
a.
b.
c.
d.
34°
30°
36°
32°
____ 20. Can you conclude that ∆ABC is congruent to ∆XYZ?
a.
b.
c.
d.
Yes, they are congruent: side-angle-side congruence
Yes, they are congruent: side-side-side congruence
Yes, they are congruent: angle-side-angle congruence
It is not possible to conclude they are congruent.
____ 21. Can you conclude that ∆ABC is congruent to ∆XYZ? Explain.
a.
b.
c.
d.
Yes, they are congruent: side-angle-side congruence
Yes, they are congruent: side-side-side congruence
Yes, they are congruent: angle-side-angle congruence
It is not possible to conclude they are congruent.
____ 22. State the corresponding sides and angles in this pair of congruent triangles.
a.
b.
c.
d.
AB = RS, AC = RT, ∠A = ∠R
AB = RT, AC = RS, ∠A = ∠T
BC = RS, AC = ST, ∠A = ∠S
None of the above choices are correct.
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Math 2201
Chapter 2
Review
____ 23. Can you prove these triangles are congruent? If so, how?
a.
b.
c.
d.
Yes, by SSS.
Yes, by SAS.
Yes, by ASA.
No, there is not enough information.
____ 24. Can you prove these triangles are congruent? If so, how?
a.
b.
c.
d.
Yes, by SSS.
Yes, by SAS.
Yes, by ASA.
No, there is not enough information.
____ 25. What can you deduce from the statement ∆ABC ≅ ∆DEF?
a.
b.
c.
d.
∠B = ∠C
∠B = ∠D
∠B = ∠E
none of the above
____ 26. What can you deduce from the statement ∆ABC ≅ ∆ACD?
a.
b.
c.
d.
AC = AD
AC is shorter than AD.
AC is longer than AD.
none of the above
____ 27. Which angle is equal to ∠A?
a.
b.
c.
d.
∠C
∠D
∠E
all of the above
____ 28. Which angle is equal to ∠F?
a.
b.
c.
d.
∠A
∠B
∠C
none of the above
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Math 2201
Chapter 2
Review
Short Answer
29. Use a protractor and a ruler to draw a pair of parallel lines.
30. Determine the measure of ∠ABF.
31. Determine the measure of ∠DBF.
32. Determine the values of a, b, and c.
33. Determine the values of a, b, and c.
34. Determine the values of a, b, and c.
35. Determine the values of a, b, and c.
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Math 2201
Chapter 2
Review
36. Determine the measure of ∠RQT.
37. Determine the measure of ∠NMO.
38. Given QP || MR, determine the measure of ∠MQO.
39. Determine the unknown angles.
40. Determine the value of x.
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Math 2201
Chapter 2
Review
41. Determine the value of x.
42. Determine the value of x.
43. Determine the sum of the measures of the interior angles of this 14-sided polygon.
Show your calculation.
44. Determine the sum of the measures of the angles in a 13-sided convex polygon.
Show your calculation.
45. Each interior angle of a regular convex polygon measures 156°.
How many sides does the polygon have?
46. Can you prove these triangles are congruent? If so, how?
47. Can you prove these triangles are congruent? If so, how?
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Math 2201
Chapter 2
Review
48. Can you prove these triangles are congruent? If so, how?
49. Two equilateral triangles share a side. Are the triangles congruent? Explain.
50. Isadora completed the following proof, but she made an error. Identify her error.
Isadora’s Proof
∠B = ∠E
BC = EF
AC = DF
∆ABC ≅ ∆DEF
Given angles
Given sides
Given angles
SAS
Problem
51. Are BD and FE parallel? Explain how you know.
52. Given LM || JK and ∠LMJ = ∠KMJ, prove JK = KM.
53. Prove that the sum of the three interior angles of a triangle is 180°.
Use a labelled diagram.
54. Is quadrilateral MATH a parallelogram? Explain.
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Math 2201
Chapter 2
Review
55. MO and LN are angle bisectors. What is the relationship, if any, between ∠L and ∠O? Explain.
56. Prove: ∠B = ∠E
57. Determine the length of EF. Show your reasoning.
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
D
D
D
B
B
C
A
C
A
D
D
C
D
C
B
D
D
C
C
B
A
C
A
B
A
C
C
SHORT ANSWER
29.
For example:
30.
∠ABF = 66°
31.
∠DBF = 114°
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Math 2201
Chapter 2
Review
32.
∠a = 18°, ∠b = 54°, ∠c = 27°
33.
∠a = 15°, ∠b = 30°, ∠c = 10°
34.
∠a = 84°, ∠b = 27°, ∠c = 54°
35.
∠a = 32°, ∠b = 84°, ∠c = 12°
36.
∠RQT = 86°
37.
∠NMO = 82°
38.
∠MQO = 75°
39.
∠EAD = 47°, ∠ABC = 47°, ∠ADE = 51°, ∠BCD = 51°, ∠CDA = 129°
40.
x = 21°
41.
x = 35°
42.
x = 48°
43.
180°(14 – 2) = 2160°
44.
180°(13 – 2) = 1980°
45.
15
46.
Yes, by SAS.
47.
Yes, by ASA.
48.
Yes, by SSS.
49.
Yes. Because all the measure of all the angles in both triangles is 60° and all the sides are equal in length to the common side, the triangles are
congruent.
50.
This is not an example of SAS because the matching angle is not between the pairs of matching sides. There is not enough information to conclude that
the triangles are congruent.
PROBLEM
51.
52.
53.
∠ABC = ∠FBD = 125°
Vertically opposite angles
∠EFB + ∠FBD = 162°
So, BD is not parallel to FE because the interior angles on the same side of the transversal are not supplementary.
Proof:
∠LMJ
∠LMJ
∠LMJ
JK
= ∠KMJ
= ∠MJK
= ∠LJM
= KM
Given
Alternate angles
Transitive property
Isosceles triangle
For example:
By alternate interior angles, ∠PDR = ∠DRE and ∠QDE = ∠RED.
A straight line contains 180°, so ∠PDR + ∠RDE + ∠QDE = 180°.
Substitute ∠DRE for ∠PDR and ∠RED for ∠QDE:
∠DRE + ∠RDE + ∠RED = 180°
Therefore, the sum of the three interior angles of an acute triangle is 180°.
54. It is not a parallelogram. ∠AMT does not equal ∠MTH, so alternate interior angles are not equal.
55.
180° = ∠L + 2a + b
180° = ∠O + a + 2b
∠L + 2a + b = ∠O + a + 2b
∠L = ∠O + a + 2b – 2a – b
∠L = ∠O – a + b
∠L = ∠O – (a – b)
∠O = ∠L + (a – b)
The difference between ∠O and ∠L is (a – b).
Angle sum of a triangle
Angle sum of a triangle
Transitive property
56.
∠ABC
AC
CB
∆ACB
∠B
= ∠DCE
= DC
= CE
≅ ∆DCE
= ∠E
Vertical opposite angles are equal
Given sides
Given sides
SAS
Corresponding angles in congruent triangles
57.
DE
∠D
∠E
∆DEF
DF
EF
June 2014
= HJ
= ∠J
= ∠H
≅ ∆JHI
= 48
= 55
Given sides
Given angles
If two pairs of angles are equal, then the third pair must be equal as well.
ASA
Corresponding sides in congruent triangles
Pythagorean theorem: 552 = 732 – 482
12

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