Download Ch. 4 Review

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.
2. HL has meaning only for right triangles.
3. An acute triangle is a triangle in which at least two angles are acute.
4. An obtuse triangle will sometimes have two obtuse angles.
5. SSS, SAS, ASA are the only ways to prove triangles congruent.
6. When stating congruent triangles, it doesn’t matter what order you put the letters in.
7. Two lines that are perpendicular form vertical angles.
8. If three sides of a triangle are congruent, then it can be called isosceles.
9. If the base angles of a triangle are congruent, the legs opposite them are congruent.
10. In a right triangle, the hypotenuse is the side opposite of the right angle.
11. An equilateral triangle is equiangular triangle.
12. The side opposite the right angle is called the base.
13. An acute triangle may have one or more acute angles.
14. A scalene triangle has no congruent sides.
15. The base of an isosceles triangle is shorter than a leg of the triangle.
16. Supplementary angles form a right angle.
17. If all angles are acute, they form an acute triangle.
18. Lines drawn in a diagram that are not part of the original diagram are auxiliary lines.
19. CPCTC stands for Corresponding Parts of Congruent Triangles are Circles.
20. Every equiangular triangle is isosceles.
21. If ΔABC ≅ ΔDEF, then AB ≅ EF .
22. In ΔABC, if ∠B is a right angle, then AC is the hypotenuse of the triangle.
23. An obtuse triangle has three obtuse angles.
24. Two triangles are congruent if two sides and an angle of one are congruent to two sides and an angle of the other.
25. A triangle with two congruent angles is always isosceles.
26. A right triangle could also be isosceles.
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?
28. If it is isosceles, then it has at least _________ sides congruent.
29. What triangle congruence postulate is used only for right triangles?
30. If FH ≅ FJ , name the base angles.
H
F
J
31. Write a valid inequality of the restrictions on x.
(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.
35.
36.
37. M is the midpoint of AB and CD.
A
C
M
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: ______ ≅ ______ and ______ ≅ ______
By SAS: ______ ≅ ______ and ______ ≅ ______
F
E
D
C
For numbers 39 – 43, use the diagram to the right.
R
1
39. If RI ≅ IT , what angles are congruent?
40. If TN ≅ IT , what angles are congruent?
I
2
11
4 5
10
41. If ∠1 ≅ ∠6, what segments are congruent?
8
G
42. The legs of isosceles ∆TNH are ________ and _________
43. The vertex angle of ∆RGH is __________
T
3
7
9
N
6
H
44. Solve for x and y.
45. Solve for x and y.
y°
x°
x°
46. Solve for x and y.
y°
47. Solve for x.
y°
x°
48. Solve for x.
(3x + 8)°
(2x + 20)°
72°
(4x + 10)°
40°
49. Solve for x.
47°
x°
50. Solve for x and y.
5x°
51. Given: GH ≅ KL
∠G ≅ ∠K
GI ≅ KJ
Prove: HI ≅ LJ
52. Given: ∠MNP ≅ ∠OPN
MN ≅ OP
Prove: ∆MNP ≅ ∆OPN
53. Given: ST || WV
ST ≅ WV
Prove: ∆TUS ≅ ∆VUW
(y + 12)°
G
54. Given: GJ is the altitude of HK
HG ≅ KG
Prove: ∆HGJ ≅ ∆KGJ
H
55. Given: ∠1 ≅ ∠4
BF ≅ DC
∠5 ≅ ∠6
Prove: ∆ACD ≅ ∆EFB
K
J
C
5
D
E
1
B
2
3
4
A
6
F
56. Given: ∠A ≅ ∠D
AC ≅ DB
Prove: SB ≅ SC
S
A
B
D
C
57. The perimeter of isosceles ∆RAM is greater than 28. Solve for x and determine which side is the base.
R
8
A
2x + 3
x+7
M