NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-4 Study Guide and Intervention
Similar Triangles: SSS and SAS Similarity
Use Similarity Theorems Here are two ways to show that two triangles are similar.
SSS Similarity
The measures of the corresponding side lengths of two triangles are proportional.
SAS Similarity
The measures of two side lengths of one triangle are proportional to the measures of two
corresponding side lengths of another triangle, and the included angles are congruent.
Example 1: Determine whether the triangles
Example 2: Determine whether the triangles
are similar.
are similar.
𝐴𝐶
𝐷𝐹
=9=3
6
𝐵𝐶
𝐸𝐹
=
AB
DE
= 15 = 3
8
12
2
=
10
3
4
2
3
6
= 8, so
𝑀𝑁
𝑄𝑅
=
𝑁𝑃
.
𝑅𝑆
m∠N = m∠R, so ∠N ≅ ∠R.
2
△NMP ∼ △RQS by SAS Similarity.
△ABC ∼ △DEF by SSS Similarity.
Exercises
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.
1.
2.
3.
4.
5.
Chapter 7
6.
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Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-4 Study Guide and Intervention (continued)
Similar Triangles: SSS and SAS Similarity
Use Similar Triangles Similar triangles can be used to find measurements.
Example1: △ABC ∼ △DEF. Find the values of x and y.
Example 2: A person 6 feet tall casts a 1.5-foot-long
shadow at the same time that a flagpole casts a 7-footlong shadow. How tall is the flagpole?
𝐴𝐶
𝐷𝐹
18√3
𝑥
= 𝐸𝐹
𝐵𝐶
𝐴𝐵
𝐷𝐸
= 𝐸𝐹
18
9
𝑦
18
=
=
18x = 9(18√3)
x = 9√3
𝐵𝐶
18
9
9y = 324
y = 36
The Sun’s rays form similar triangles.
6 1.5
Using x for the height of the pole, 𝑥 = 7 ,
so 1.5x = 42 and x = 28.
The flagpole is 28 feet tall.
Exercises
ALGEBRA Identify the similar triangles. Then find each measure.
1. NQ
2. VW
3. QR
4. IU
5. POSTS The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is
0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth?
Chapter 7
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Glencoe Geometry