Geometry CC
Assignment #51
Similarity and Angle Bisector Theorem
1. The sides of a triangle have lengths of 12, 16, and 21.
An angle bisector meets the side of length 21.
Find the lengths of x and y.

2. The perimeter of UVW is 22.5. WZ bisects
UWV , UZ = 2, and VZ = 2.5. Find UW and VW.
3. The sides of a triangle have lengths of 5, 8 and 6.5. An angle bisector meets the side of
length 6.5. Find the lengths of both parts that make up the length of 6.5.
4. The sides of a triangle are 10.5, 16.5, and 9. An angle bisector meets the side of length 9.
Find lengths of the two parts that make up the length of 9.
5. In the diagram of DEF below, DG is an angle bisector,
1
DE = 8, DF = 6, and EF = 8 . Find FG and EG.
6
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6. Given CD = 3, DB = 4, BF = 4, FE = 5, AB = 6 and CAD  DAB  BAF  FAE , find
the perimeter of quadrilateral AEBC. [Find the lengths of CA and AE first.]
R1. Three angles of a triangle are represented by 3x + 5, 2x – 7 and 2x.
What is the measure of the smallest angle of the triangle?
R2. A 20-foot pole that is leaning against a wall reaches a point that is 18 feet above the
ground. Find to the nearest degree, the measure of the angle that the pole makes with the
ground.
R3. Simplify:
125
R4. Given the diagram, CAB  CFE . Find AB.
1.
2.
3.
4.
x = 9, y = 12
UW = 8, VW = 10
2.5 and 4
5.5 and 3.5
2
1
5. GE  4 and FG  3
3
2
6. CA = 4.5 and EA = 7.5, Perimeter = 28
R1.
R2.
R3.
R4.
45
68 degrees
5 5
7.5
Island Trees Math Department