Download Ch. 4 Rev Answers

Honors Geometry
Chapter 4 Review
Name: _____________________________________
For numbers 1 – 26, determine whether the statement is true or false.
1. CPCTC means Can Pete cut Tracy’s Chin. F
2. HL has meaning only for right triangles. T
3. An acute triangle is a triangle in which at least two angles are acute. F
4. An obtuse triangle will sometimes have two obtuse angles. T
5. SSS, SAS, ASA are the only ways to prove triangles congruent. F
6. When stating congruent triangles, it doesn’t matter what order you put the letters in. F
7. Two lines that are perpendicular form vertical angles. T
8. If three sides of a triangle are congruent, then it can be called isosceles. T
9. If the base angles of a triangle are congruent, the legs opposite them are congruent. T
10. In a right triangle, the hypotenuse is the side opposite of the right angle. T
11. An equilateral triangle is equiangular triangle. T
12. The side opposite the right angle is called the base. F
13. An acute triangle may have one or more acute angles. F
14. A scalene triangle has no congruent sides. T
15. The base of an isosceles triangle is shorter than a leg of the triangle. F
16. Supplementary angles form a right angle. F
17. If all angles are acute, they form an acute triangle. T
18. Lines drawn in a diagram that are not part of the original diagram are auxiliary lines. T
19. CPCTC stands for Corresponding Parts of Congruent Triangles are Circles. F
20. Every equiangular triangle is isosceles. T
21. If ΔABC ≅ ΔDEF, then AB ≅ EF . F
22. In ΔABC, if ∠B is a right angle, then AC is the hypotenuse of the triangle. T
23. An obtuse triangle has three obtuse angles. F
24. Two triangles are congruent if two sides and an angle of one are congruent to two sides and an angle of the other. F
25. A triangle with two congruent angles is always isosceles. T
26. A right triangle could also be isosceles. T
27. If you were trying to prove ∆ABC ≅ ∆DEF by ASA and were given ∠A ≅ ∠D and ∠C ≅ ∠F, what sides would you need
congruent? AC ≅ DF
28. If it is isosceles, then it has at least ___2_____ sides congruent.
29. What triangle congruence postulate is used only for right triangles? HL
30. If FH ≅ FJ , name the base angles.
H
∠H ≅ ∠J
F
J
31. Write a valid inequality of the restrictions on x.
0< x<
10
3
(5x – 10)°
(2x)°
For numbers 32 – 37, state the reason the following triangles are congruent. If they are not congruent, then state “not possible”.
32.
33.
34.
HL
SSS
Not Possible
35.
36.
37. M is the midpoint of AB and CD.
A
C
M
Not Possible
Not Possible
SAS D
B
38. State the missing sides or angles that we would need to have congruent, to prove the triangles congruent by the method indicated.
A
∆AFE ≅ ∆BCD
B
By ASA: _∠FAE__ ≅ _∠CBD_ and _∠FEA_ ≅ _∠CDB_
By SAS: _∠FAE__ ≅ _∠CBD_ and _ AF _ ≅ _ BC _
OR
F
E
D
C
By SAS: _∠AEF__ ≅ _∠BDC_ and _ FE _ ≅ _ DC _
For numbers 39 – 43, use the diagram to the right.
R
1
39. If RI ≅ IT , what angles are congruent? ∠1 & ∠3
40. If TN ≅ IT , what angles are congruent? ∠11 & ∠8
2
I
T
3
11
4
10
41. If ∠1 ≅ ∠6, what segments are congruent? RG & GH
8
G
42. The legs of isosceles ∆TNH are __ TN ____ and ___ NH ____
5
9
7
N
6
H
43. The vertex angle of ∆RGH is ____G_____
44. Solve for x and y.
45. Solve for x and y.
x = 45
y = 135
x = 60
y = 120
x°
y°
x°
y°
46. Solve for x and y.
47. Solve for x.
y°
x = 72
y = 36
(3x + 8)°
x = 18
x°
(2x + 20)°
72°
48. Solve for x.
49. Solve for x.
(4x + 10)°
x = 22.5
x = 33.25
40°
47°
x°
50. Solve for x and y.
x=9
y = 33
5x°
(y + 12)°
51. Given: GH ≅ KL
∠G ≅ ∠K
GI ≅ KJ
Prove: HI ≅ LJ
Statements
1. GH ≅ KL
2. ∠G ≅ ∠K
3. GI ≅ KJ
4. ∆HGI ≅ ∆LKJ
5. HI ≅ LJ
Reasons
1. Given
2. Given
3. Given
4. SAS
5. CPCTC
52. Given: ∠MNP ≅ ∠OPN
MN ≅ OP
Prove: ∆MNP ≅ ∆OPN
Statements
1. ∠MNP ≅ ∠OPN
2. MN ≅ OP
3. NP ≅ NP
4. ∆MNP ≅ ∆OPN
Reasons
1. Given
2. Given
3. Reflexive Property
4. SAS
53. Given: ST || WV
ST ≅ WV
Prove: ∆TUS ≅ ∆VUW
Statements
Reasons
1. Given
1. ST ≅ WV
2. ST || WV
2. Given
3. ∠W ≅ ∠S
4. ∠T ≅ ∠V
5. ∆TUS ≅ ∆VUW
3. Alternate Interior Angles
4. Alternate Interior Angles
5. ASA
G
54. Given: GJ is the altitude of HK
HG ≅ KG
Prove: ∆HGJ ≅ ∆KGJ
H
K
J
Statements
Reasons
1. Given
1. GJ is the altitude of HK
2. ∠HJG and ∠KJG are right angles
3. ∆HJG and ∆KJG are right triangles
2. Definition of perpendicular
3. Definition of right triangle
4. Given
4. HG ≅ KG
5. JG ≅ JG
6. ∆HGJ ≅ ∆KGJ
55. Given: ∠1 ≅ ∠4
BF ≅ DC
∠5 ≅ ∠6
Prove: ∆ACD ≅ ∆EFB
5. Reflexive Property
6. HL
C
5
D
3
4
E
1
B
2
A
6
F
Statements
1. ∠1 ≅ ∠4
2. ∠1 is supp. to ∠2
3. ∠4 is supp. to ∠3
4. ∠2 ≅ ∠3
5. BF ≅ DC
6. ∠5 ≅ ∠6
7. ∆ACD ≅ ∆EFB
Reasons
1. Given
2. Linear Pair Postulate
3. Linear Pair Postulate
4. Congruent Supplements Theorem
5. Given
6. Given
7. ASA
56. Given: ∠A ≅ ∠D
AC ≅ DB
Prove: SB ≅ SC
S
A
B
D
C
Statements
1. ∠A ≅ ∠D
Reasons
1. Given
2. AS ≅ SD
3. AC ≅ DB
2.
3. Given
4. BC ≅ BC
4. Reflexive Property
5. AB ≅ DC
6. ∆SAB ≅ ∆SDC
5. Subtraction Property
6. SAS
7. CPCTC
7. SB ≅ SC
57. The perimeter of isosceles ∆RAM is greater than 28. Solve for x and determine which side is the base.
x>
R
10
3
RA is the base
8
A
2x + 3
x+7
M