This document discusses using similar triangles to solve problems involving proportions. It begins with examples of identifying similar triangles in diagrams and writing proportions between corresponding sides. It then shows how to use proportions to find unknown side lengths. One example finds the maximum depth of a swimming pool using similar right triangles formed by the pool diagram. Another finds the value of y in a right triangle given side lengths using a proportion of corresponding hypotenuses and shorter legs. The document concludes with an example using similar triangles to approximate the height of a gym wall.

1. 7.3 Use Similar Right Triangles
7.3
Bell Thinger
1. Are these triangles similar? If so, give the reason.
ANSWER
2. Find x.
Yes; the AA Similarity Postulate
ANSWER
50

2. 7.3

3. Example 1
7.3
Identify the similar triangles in the diagram.
SOLUTION
Sketch the three similar right triangles so that the
corresponding angles and sides have the same orientation.
TSU ~
RTU ~
RST

4. Example 2
7.3
Swimming Pool The diagram below shows a crosssection of a swimming pool. What is the maximum
depth of the pool?

5. Example 2
7.3
SOLUTION
STEP 1 Identify the similar triangles and sketch them.
RST ~ RTM ~ TSM
STEP 2
Find the value of h. Use the fact that RST ~
RTM
to write a proportion.
Corresponding side lengths of
TM TR
=
similar triangles are in proportion.
ST
SR
h
152
=
Substitute.
64
165
165h = 64(152)
h ≈ 59
Cross Products Property
Solve for h.

6. Example 2
7.3
STEP 3
Read the diagram. You can see that the maximum
depth of the pool is h + 48, which is about 59 + 48 = 107
inches.
The maximum depth of the pool is about 107 inches.

7. Guided Practice
7.3
Identify the similar triangles. Then find the value of x.
1.
ANSWER
EGF ~
GHF ~
LMJ ~
MKJ ~
EHG ;
12
5
2.
ANSWER
LKM ;
60
13

8. Example 3
7.3
Find the value of y. Write your
answer in simplest radical form.
SOLUTION
STEP 1
Draw the three similar triangles.

9. Example 3
7.3
STEP 2
Write a proportion.
length of hyp. of
length of hyp. of
RPQ length of shorter leg of
=
RQS length of shorter leg of
9
y
y
= 3
RPQ
RQS
Substitute.
27 = y2
Cross Products Property
27 = y
Take the positive square
root of each side.
3 3=y
Simplify.

10. 7.3

11. Example 4
7.3
Rock Climbing Wall
To find the cost of installing a
rock wall in your school
gymnasium, you need to find
the height of the gym wall.
You use a cardboard square to
line up the top and bottom of
the gym wall. Your friend
measures the vertical distance
from the ground to your eye
and the distance from you to
the gym wall. Approximate the
height of the gym wall.

12. Example 4
7.3
SOLUTION
By Theorem 7.6, you know that 8.5 is the geometric
mean of w and 5.
w
8.5
8.5 = 5
w ≈ 14.5
Write a proportion.
Solve for w.
So, the height of the wall is 5 + w ≈ 5 + 14.5 = 19.5 feet.

13. Guided Practice
7.3
3.
Mary is 5.5 feet tall. How far from the wall in
Example 4 would she have to stand in order to
measure its height?
ANSWER
about 8.93 ft

14. Exit Slip
7.3
1.
Identify the three similar right triangles in the
diagram.
ANSWER
XYZ ~
XWY ~
YWZ

15. Exit Slip
7.3
Find the value of the variable.
2.
ANSWER
3 5

16. Exit Slip
7.3
Find the value of the variable.
3.
ANSWER
2 15

17. 7.3
Homework
Pg 471-474
#6, 14, 18, 23, 30