warm-up exercises answer yes; the aa similarity postulate 1. are these triangles similar? if so,...

Warm-Up Exercises

ANSWER Yes; the AA Similarity Postulate

1. Are these triangles similar? If so, give the reason.

Warm-Up Exercises

ANSWER 50

2. Find x.

Warm-Up ExercisesEXAMPLE 1 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-Up ExercisesEXAMPLE 2 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?


STEP 1Identify the similar triangles and sketch them.

RST ~ RTM ~ TSM

SOLUTION


64 h

=165152

Substitute.

165h = 64(152) Cross Products Property

h 59 Solve for h.

STEP 3Read 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.

STEP 2Find the value of h. Use the fact that RST ~ RTM to write a proportion.

STTM

=SRTR Corresponding side lengths of

similar triangles are in proportion.

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Identify the similar triangles. Then find the value of x.

1.

EGF ~ GHF ~ EHG ; 12 5

ANSWER

2.

LMJ ~ MKJ ~ LKM ; 60 13

ANSWER

Warm-Up ExercisesEXAMPLE 3 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-Up ExercisesEXAMPLE 3 Use a geometric mean

STEP 2 Write a proportion.

length of hyp. of RQSlength of hyp. of RPQ

=length of shorter leg of RQSlength of shorter leg of RPQ

y9

= 3y

27 = y2

27 = y

3 3 = y Simplify.

Take the positive square root of each side.

Substitute.

Cross Products Property

Warm-Up ExercisesEXAMPLE 4 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-Up ExercisesEXAMPLE 4 Find a height using indirect measurement

SOLUTION

By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5.

8.5w

= 58.5

Write a proportion.

w 14.5 Solve for w.

So, the height of the wall is 5 + w 5 + 14.5 = 19.5 feet.


3. In Example 3, which theorem did you use to solve for y ? Explain.

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.

ANSWER


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

Warm-Up ExercisesDaily Homework Quiz

1. Identify the three similar right triangles in the diagram.

ANSWER XYZ ~ XWY ~ YWZ


2.

Find the values of the variable.

ANSWER 3 5


2 15ANSWER

3.

Find the values of the variable.

warm-up exercises answer yes; the aa similarity postulate 1. are these triangles similar? if so,...

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