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Problem 1
Fill in the blank(s) to correctly complete each sentence.
The sum of the measures of the angles of any triangle is ________________ .
Problem 2
Fill in the blank(s) to correctly complete each sentence.
An isosceles right triangle has one ________________ angle and ______________ equal sides.
Problem 3
Fill in the blank(s) to correctly complete each sentence.
An equilateral triangle has _________________ equal sides.
Problem 5
CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.
Problem 6
CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.
Problem 7
CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles.
Problem 8
CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles.
Problem 9
CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (EA is parallel to CD.)
Problem 10
CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (HK is parallel to EF.)
Problem 11
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 12
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 13
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
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Problem 14
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 15
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel.
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Problem 16
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 18
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 20
Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
Problem 23
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°
Problem 25
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 147° 12' , 30° 19'
Problem 28
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
29.6° , 49.7°
Problem 30
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
17° 41' 13" , 96° 12' 10"
Problem 36
Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.
Problem 39
Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.
Problem 43
Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.
Problem 57
Find the unknown side lengths in each pair of similar triangles. See Example 4.
Problem 62
Solve each problem. See Example 5. Height of a Lighthouse The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 A.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?
Problem 63
Solve each problem. See Example 5. Height of a Building A house is 15 ft tall. Its shadow is 40 ft long at the same time that the shadow of a nearby building is 300 ft long. Find the height of the building.
Problem 64
Solve each problem. See Example 5. Height of a Carving of Lincoln Assume that Lincoln was 6 1/3 ft tall and his head was 3/4 ft long. Knowing that the carved head of Lincoln at Mt. Rushmore is 60 ft tall, find how tall his entire body would be if it were carved into the mountain.
Problem 67
In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.
Problem 69
Solve each problem. Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon's umbra (shadow) to reach the surface of Earth. (Data from Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) a. Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.)