# Document 17613160 ```Part I. Fill in the blank.
1. In a triangle, the smallest angle is across from __________________________________________.
2. _____, _____, _____, _____, _____ are the five methods to prove triangles congruent.
4. Equiangular triangles are also ________________________________.
5. Corresponding parts of congruent triangles are _______________________________.
7. The hypotenuse of a right triangle is opposite the ____________________________________.
8. If two sides of a triangle have length 4 and 6 then the third side must be between ____ and ____.
Fill in the blank with Always, Sometimes, or Never.
1. Isosceles triangles are acute. _____
2. An acute triangle is equilateral. _____
3. A scalene triangle is obtuse. _____
4. A right triangle is isosceles. _____
Find the value of x.
5.
6.
5x
(4x - 3)
(7x + 9)
27
34
49
(3x + 56)
Determine which postulate or theorem can be used to prove the triangles are congruent.
7.
8.
9.
Find the value of x and y.
10.
11.
12.
70
y
4y
x
x
49
x
24
y
13. What is the vertex of  ABC? __________
Write the inequality relating each pair of measures.
1. m  PRQ _______ m  PRS
2. m  DBC ________ m  ABE
B
R
7
Q
15
7
5
P
15
12
9
S
12
A 4 E
D 6 C
3. Use the figure to the right to write an inequality to describe the possible values of x.
R
10
Q
12
15 (2x - 5)
55
P
15
4. The measures of the angles in a triangle are in the extended ratio 1:4:7. Find the measures of the
angles.
_____ _____ _____
Solve each proportion.
5
4
5.

x3 x
7. Given that ABC
Find the geometric mean of the two numbers.
6. 3 and 27
DEF, use the diagram to find the values of x and y.
17. Luke Skywalker is 5 feet 9 inches tall. He casts a shadow that is 3 feet 4 inches long. R2D2 casts
a shadow that is 28 inches long. How tall is R2D2? C3PO is 69 inches tall. How long is his shadow?
S
8. The dotted segment is a special segment in similar triangles. Find the value of the variable.
14
18
27
z-4
Find the value of the variable.
9.
10.
7
10
12
h
g
24
8
12
Part III. Proofs
Complete each proof.
JK  JL
2. GIVEN:
K
M is the midpoint of KL
PROVE:
J
K  L
M
L
Statements
Reasons
1.
1. Given
2. M is the midpoint of KL
2.
3.
3. Definition of a midpoint
4.
4. Reflexive property
5.
5. SSS
6. K  L
6.
Complete the following proof. (not drawn to scale)
G
GIVEN:
82
GK = 2
GJ = 30
GF = 6
FH = 4
GKF
PROVE:
K
J
Statements
Reasons
1.
1. Given
2. GJ = 30
2.
3. GF = 6
3.
3.
4. Given
4. GF + FH = GH
5.
6.
6. Substitution Property
7.
7. Combine like terms
2 3 6
 
10 3 30
2
6

9.
10 30
GK GF

10.
GH GJ
11. G ≅ G
12. GKF
GHJ
F
50
GHJ
8.
48
8.
9.
10.
11. Reflexive Property
12.
H
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