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1. In the figure below, m<B = 40o, m<X = 60o, and m<Z = 80o.
What reason could prove that ABC and XYZ are similar?
2.
3. If <A = <X and <B = <Y,
a. What reasons could prove the two triangles are congruent?
b. What reasons would NOT prove the two triangles are congruent?
4. Name all pairs of consecutive interior angles.
5. A ladder is leaning against a house, which is 20 feet tall. What is the approximate length of the
ladder to the nearest foot?
6. What is the measure of side PQ to the nearest tenth?
7. Triangle ABC is a right triangle. The measure of angle A is 30o. What is the length of side AC?
8. List the angles from least to greatest.
9. List the angles from largest to smallest
21. Which lists the sides of
10. List the sides from largest to smallest.DBCD in order from
11. List
the sides to
from shortest to longest.
shortest
longest?
A
B
C
D
CD,
BC,
BD,
BC,
BD,
CD,
CD ,
BD ,
BC
BD
BC
CD
22
G0921B2-Triangles & Logic
12. Given two sides of a triangle measure 14 inches and 8 inches. Select the three lengths that
could be the measure of the third side.
3 inches
6 inches
10 inches
13 inches
15.5 inches
22 inches
25 inches
13. The side lengths of a triangle are 20 and 35. Which could NOT be the length of the third side?
16
40
50
55
14. Circle all of the following that could be the lengths of the sides of a triangle.
3, 5, 7
2, 2, 4
6, 10, 2
7, 4, 5
5, 10, 4
15.
16. What is the inverse of the conditional statement? Determine whether the inverse is true or false. If
it is false, find a counterexample.
People who live in Texas live in the United States.
A People who live in the United States live in Texas. False; they could live in
Oklahoma.
B People who do not live in the United States do not live in Texas. True
C People who do not live in Texas do not live in the United States. False; they could
live in Oklahoma.
D People who do not live in Texas live in the United States. True
17. Find the value of x. Then find the length of AE.
x = ___________________________
AE = ___________________________
18. Which of the following correctly describes the relationship between the sides of the triangles below?
AE
AB
AB
AE
AB
AE
ED
EC
CD
EC
CD
ED
19.. In this figure, AC and BD bisect each other. Based on the information given, which triangle
congruence theorem could be used to prove AED = CEB?
A.
B.
C.
D.
AAS
ASA
SAS
SSS
20. IF MNO = PQR, which of the following can you NOT conclude as being true? (DRAW A PICTURE!)
DRAW PICTURE HERE:
21.
23. Can 15, 10 and 10 be the lengths of the sides of a right triangle? Explain.
24. Complete the reasons in the following
proof:
Reasons:
Given
Def. of Midpoint
CPCTC
Def. of Bisector
Vertical Angles
Reflexive Property
Alternate Interior Angles
SSS-SAS-ASA-AAS
Statements
Reasons
̅̅̅̅
̅̅̅̅ ≅ 𝑄𝐾
1) 𝑃𝐾
1) ________________________________
2) ̅̅̅̅
𝐾𝐿 bisects PKQ
2) ________________________________
3) PKL  QKL
3) ________________________________
4) ̅̅̅̅
𝐾𝐿 ≅ ̅̅̅̅
𝐾𝐿
4) ________________________________
5) PKL  QKL
5) ________________________________
6) <P = <Q
6) ________________________________
25. Name whether the triangles are congruent by SSS, SAS, ASA, AAS or if they are not congruent
_________________________
_________________________
_________________________
________________________
26. If the coordinates of A are (6, 2) and the midpoint of AB is (3, 1) then what are the coordinates of B?
27. The lengths of two sides of DABC are 30 in. and 44 in. Which of the following could NOT be the length
of the third side? Select all values.
14
15
36
74
79
28. Order the sides of triangle QRS from shortest to longest.
29. Line m contains points (1, -3) and (2, 2). Which of the following pairs of points define a line parallel to
line m?
(-4, 0) and (5, 5)
(1, 1) and (6, 2)
(0, 0) and (1, 5)
(0,0) and (-1, 1)