Chapter 7 Practice
1) Draw a trapezoid that has legs of length 24 and 18. A third line, parallel to the two bases, is drawn
inside the trapezoid. This new line cuts one leg into pieces of length 10 and 14. How large are the pieces
that the second leg is cut into?
2) In triangle ABC, AB  x, BC  y, and AC  28. The perimeter of triangle ABC is 36.
a) If the angle bisector from angle B splits AC into pieces of 7 and 21, find x and y.
b) What’s wrong with this problem?
3) The following figures are similar. Find the value(s) of the unknown variables in each.
(Use your inner dialogue.)
a)
9
13
4
b)
2x-5
x
x-1 53
2x
12
37
4) Show that the given information is impossible.
Given: US bisects NUR
NR bisects SNU
RU=4, BR=5
SB=6, NS=7
R
B
5) Show that the area of the triangle equals
a
c
b
x
d
U
S
1
2
a ab  12 b ab
N
Chapter 7 Additional Review
Find the value of the variables. Show all work.
1. Find the geometric mean of 32 and 4.
2.
z
y
3.
y
4.
15
12
x  15
x
R
5.
P
6.
6
S
12
20
x
36
10
17
x
Q
24
x 1 x 1

6
x
7. Identify the triangle similarity postulate that explains why the triangles are similar. Then, write a
similarity statement for each pair.
a)
b)
BAX 
8. The perimeter of a given triangle is 42cm. If the ratio of the sides is 3:4:5, find the lengths of the three
sides.
9. Find the perimeter of the large triangle.
7
2
x
x
3
x+4
2
y
10. The polygons below are similar. Find the values of x and y.
10
20
12
8
y3
16
18
x2