1. Five-Minute Check (over Lesson 7–3) Mathematical Practices Then/Now
Theorem 7.3: SSS Triangle Similarity
Theorem 7.4: SAS Triangle Similarity
Example 1: Use the SSS Theorem
Example 2: Analyze Triangles on the Coordinate Plane
Key Concept: Corresponding Parts of Similar Triangles
Example 3: Use the SAS Similarity Theorem
Example 4: Analyze Triangles on the Coordinate Plane
Example 5: Indirect Measurement
Lesson Menu

2. Determine whether the triangles are similar. Justify your answer.
A. yes, SSS Similarity
B. yes, ASA Similarity
C. yes, AA Similarity
D. No, sides are not proportional.
5-Minute Check 1

3. Determine whether the triangles are similar. Justify your answer.
A. yes, AA Similarity
B. yes, SSS Similarity
C. yes, SAS Similarity
D. No, sides are not proportional.
5-Minute Check 2

4. Determine whether the triangles are similar. Justify your answer.
A. yes, AA Similarity
B. yes, SSS Similarity
C. yes, SAS Similarity
D. No, angles are not equal.
5-Minute Check 3

5. Find the width of the river in the diagram.
B. 28 m
C. 24 m
D m
5-Minute Check 4

6. Mathematical Processes
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure. MP

7. G.SRT.4 Prove theorems about similarity.
Content Standards
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.4 Prove theorems about similarity.
G.SRT.5 Use congruence and similarity for triangles to solve problems and to prove relationships in geometric figures. MP

8. You used the AA Similarity Postulate to prove triangles are similar.
Use the SSS similarity criterion to prove triangles are similar.
Use the SAS similarity criterion to prove triangles are similar.
Then/Now

9. Theorem

10. Theorem

11. Use the SSS Theorem
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. A.
Example 1A

12. Answer: ABC ∼ DEC by the SSS Similarity Theorem.
Use the SSS Theorem
Write a proportion that relates to the corresponding sides.
Substitute the lengths of the sides.
Simplify
SSS Similarity Theorem
Answer: ABC ∼ DEC by the SSS Similarity Theorem.
Example 1A

13. Use the SSS Theorem
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. B.
Example 1B

14. Answer: The sides are not proportional, so MNO WXY.
Use the SSS Theorem
Write a proportion that relates to the corresponding sides.
Substitute the lengths of the sides.
Simplify
∆MNO is not similar ∆WXY.
SSS Similarity Theorem does not apply.
Answer: The sides are not proportional, so MNO WXY.
Example 1B

15. Analyze Triangles on the Coordinate Plane
Determine whether DEF with vertices D(–4, 0), E(6, –1), and F(3, 3) is similar to LMN with vertices L(–3, –5), M(15, –7), and N(11, –1). Explain your reasoning.
Graph the points and determine the corresponding sides.
Write a proportion that relates to the corresponding sides.
Find the side lengths by using the distance formula.
Example 2

16. Answer: The sides are not proportional, so DEF LMN.
Analyze Triangles on the Coordinate Plane
Substitute the lengths of the sides.
∆DEF is not similar ∆LMN.
The sides are not proportional.
Answer: The sides are not proportional, so DEF LMN.
Example 2

17. Key Concept

18. Use the SAS Similarity Theorem
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. A.
Example 3

19. Use the SAS Similarity Theorem
Do you have enough information to write a proportion that relates to the corresponding sides? No
Do the triangles have congruent corresponding angles? No
The triangles are not similar because the sides are not proportional and the corresponding angles are not congruent.
Answer: The triangles are similar, because the sides are not proportional and the angles are not congruent.
Example 3

20. Use the SAS Similarity Theorem
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. B.
Example 3

21. Answer: MNP ∼ MRS by the SAS Similarity Theorem.
Use the SAS Similarity Theorem
Write a proportion that relates to the corresponding sides.
Substitute the lengths of the sides.
∠M ≅ ∠M
The Reflexive Property
SAS Similarity Theorem
Answer: MNP ∼ MRS by the SAS Similarity Theorem.
Example 3

22. Analyze Triangles on the Coordinate Plane
Determine whether WUV with vertices W(–2, 5), U(2, –6), and V(3, 5) is similar to WXY with vertices X(10, –28), and Y(13, 5). Explain your reasoning.
Graph the points and determine the corresponding sides.
Write a proportion that relates to the corresponding sides.
Find the side lengths by using the distance formula.
Example 4

23. Answer: WUV  WXY by SAS Similarity
Analyze Triangles on the Coordinate Plane
Substitute the lengths of the sides.
Simplify
∠W ≅ ∠W
The Reflexive Property
SAS Similarity Theorem
Answer: WUV  WXY by SAS Similarity
Example 4

24. Joaquin wants to measure the height of a building
Indirect Measurement
Joaquin wants to measure the height of a building
obstructing his view of the lake. He stands so that
the tip of his shadow coincides with the tip of the building’s shadow. He is 5 feet 6 inches tall, and his shadow is 18 feet long at the same time that the building’s shadow is 360 feet long. About how tall is the building?
Example 5

25. Indirect Measurement
Write a proportion that relates to the corresponding sides.
Solve for x.
Answer: 110 feet
Example 5