Name_________________________________________________ Period__________ Date________________
Geometry Chapter 5 Review
1. Line segment BT is the bisector of ∠ABC, AT is the bisector of ∠BAC, and TC is the bisector of ∠ACB.
If MT = 13, m∠MBT = 2x – 7, and m∠TBL = 25°, find the length of LT and the value of x.
B
L
M
T
A
C
N
LT = __________
x = __________
2. The vertices of ΔJLK are J(-9, 2), K(10, 1), and L(5,6). AB is the midsegment parallel to KL. What is the length
y
of AB?
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
8
10
x
-2
-4
-6
-8
-10
3. List the angles of the triangle below in order
from smallest to largest.
A
A
6
10
C
4. List the sides of the triangle below in order from
shortest to longest.
B
12
C
63°
51°
B
5. Determine whether each set of side lengths could construct a triangle. Circle yes or no.
a. 5, 7, 10
Yes or No
b. 8, 8, 16
Yes or No
c. 10, 7, 2
Yes or No
6. Give the range of values that could represent the third side of a triangle with the given two lengths.
a. 5 and 12
Range:____________
b. 22 and 8
Range:____________
7. Answer the following questions about the triangle drawn below. Given X, Y, and Z are the midpoints of their
respective sides.
B
a. What type of segments are XY, ZY, and XZ
14
8
______________________________
X
b. Perimeter of ΔABC _______________
Z
8
C
d. If the area of ΔABC = 64,
area of ΔXYZ =______________
Y
22
A
c. Perimeter of ΔXYZ _______________
8. Answer the following questions about the triangle drawn below. Given D, E, and F are the midpoints of
their respective sides.
B
a. What type of segments are BD, CE, and AF
______________________________
b. Point z is known as the _________________
E
F
c. If ZF = 3, then AF = _______, AZ = ________
Z
d. If BD = 18, then DZ = _______, BZ = _______
A
e. If CZ = 8, then ZE = _______, EC = ________
D
C
f. If AE = 3x - 1, and BE = x + 9, x = ___________
9) Could the following lengths represent a right triangle?
6, 8, 10
yes no
15, 20, 30
yes no
10) Determine the height, x, of the trapezoid in the figure below.
x
11) Find the length of a diagonal of a square if the perimeter of the square is 16. Leave your answer in
simplest radical form (not a decimal).
12) The perimeter of an equilateral triangle is 30 3 . What is the length of each side of the triangle?
13) The diagonal of a rectangle is 25 in. If the height of the rectangle is 7, how long is the width?
14. RT and TS are perpendicular bisectors of ΔABC. What is the perimeter of ΔATC?
5.3
3.5
4.8
15. Lines j and k contain medians of ΔDEF. Determine the value of y.
16. In the accompanying diagram, ΔABC is an equilateral triangle with a perimeter of 24 inches.
What is the length of the altitude, h, of this triangle?
17. The right triangle shown below is formed by joining three squares at their vertices.
What is the value of z, the side length of the bottom square?
225 cm2
9 cm
z