Warm-Up Exercises
1. Are these triangles similar? If so, give the reason.
ANSWER
Yes; the AA Similarity Postulate
Warm-Up Exercises
2. Find x.
ANSWER
50
Warm-Up1Exercises
EXAMPLE
Identify similar triangles
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
Warm-Up2Exercises
EXAMPLE
Find the length of the altitude to the hypotenuse
Swimming Pool
The diagram below shows a cross-section of a
swimming pool. What is the maximum depth of the
pool?
Warm-Up2Exercises
EXAMPLE
Find the length of the altitude to the hypotenuse
SOLUTION
STEP 1
Identify the similar triangles and sketch them.
RST ~
RTM ~
TSM
Warm-Up2Exercises
EXAMPLE
Find the length of the altitude to the hypotenuse
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
Cross Products Property
165h = 64(152)
Solve for h.
h
59
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.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Identify the similar triangles. Then find the value of x.
1.
ANSWER
EGF ~
2.
GHF ~
EHG ; 12
5
MKJ ~
LKM ; 60
13
ANSWER
LMJ ~
Warm-Up3Exercises
EXAMPLE
Use a geometric mean
Find the value of y. Write your
answer in simplest radical form.
SOLUTION
STEP 1
Draw the three similar triangles.
Warm-Up3Exercises
EXAMPLE
Use a geometric mean
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
3
y
= 3
RPQ
RQS
Substitute.
27 = y2
Cross Products Property
27 = y
Take the positive square
root of each side.
3=y
Simplify.
Warm-Up4Exercises
EXAMPLE
Find a height using indirect measurement
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.
Warm-Up4Exercises
EXAMPLE
Find a height using indirect measurement
SOLUTION
By Theorem 7.6, you know that 8.5 is the geometric
mean of w and 5.
w
8.5
8.5 = 5
Write a proportion.
w
Solve for w.
14.5
So, the height of the wall is 5 + w
5 + 14.5 = 19.5 feet.
Warm-Up
Exercises
GUIDED
PRACTICE
3.
for Examples 3 and 4
In Example 3, which theorem did you use to
solve for y ? Explain.
ANSWER
Theroem 7.7; This was used to set the ratios of the
hypotenuse of the large triangle to the shorter leg and
the hypotenuse of the small triangle to the shorter leg
equal to each other.
Warm-Up
Exercises
GUIDED
PRACTICE
4.
for Examples 3 and 4
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
Daily
Homework
Quiz
Warm-Up
Exercises
1.
Identify the three similar right triangles in the
diagram.
ANSWER
XYZ ~
XWY ~
YWZ
Daily
Homework
Quiz
Warm-Up
Exercises
Find the values of the variable.
2.
ANSWER
3 5
Daily
Homework
Quiz
Warm-Up
Exercises
Find the values of the variable.
3.
ANSWER
2 15