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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?
Warm-Up ExercisesEXAMPLE 2 Find the length of the altitude to the hypotenuse
STEP 1Identify the similar triangles and sketch them.
RST ~ RTM ~ TSM
SOLUTION
Warm-Up ExercisesEXAMPLE 2 Find the length of the altitude to the hypotenuse
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.
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
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
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
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
Warm-Up ExercisesDaily Homework Quiz
2.
Find the values of the variable.
ANSWER 3 5
Warm-Up ExercisesDaily Homework Quiz
2 15ANSWER
3.
Find the values of the variable.
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