The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar

New York State Common Core Math Geometry, Module 2, Lesson 17

Worksheets for Geometry

Student Outcomes

• Students prove the side-angle-side criterion for two triangles to be similar and use it to solve triangle problems.
• Students prove the side-side-side criterion for two triangles to be similar and use it to solve triangle problems.

The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar

Classwork

Opening Exercise

a. Choose three lengths that represent the sides of a triangle. Draw the triangle with your chosen lengths using construction tools.
b. Multiply each length in your original triangle by 2 to get three corresponding lengths of sides for a second triangle. Draw your second triangle using construction tools.
c. Do your constructed triangles appear to be similar? Explain your answer.
d. Do you think that the triangles can be shown to be similar without knowing the angle measures?

• Show Video for Whole Lesson

Exploratory Challenge 1/Exercises 1–2

1. Examine the figure, and answer the questions to determine whether or not the triangles shown are similar.
   a. What information is given about the triangles in Figure 1?
   b. How can the information provided be used to determine whether △ 𝐴𝐵𝐶 is similar to △ 𝐴𝐵′𝐶′?
   c. Compare the corresponding side lengths of △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′. What do you notice?
   d. Based on your work in parts (a)–(c), draw a conclusion about the relationship between △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′.
   Explain your reasoning.
2. Examine the figure, and answer the questions to determine whether or not the triangles shown are similar.
   a. What information is given about the triangles in Figure 2?
   b. How can the information provided be used to determine whether △ 𝑃𝑄𝑅 is similar to △ 𝑃𝑄′𝑅′?
   c. Compare the corresponding side lengths of △ 𝑃𝑄𝑅 and △ 𝑃𝑄′𝑅′. What do you notice?
   d. Based on your work in parts (a)–(c), draw a conclusion about the relationship between △ 𝑃𝑄𝑅 and △ 𝑃𝑄′𝑅′. Explain your reasoning.

Exploratory Challenge 2/Exercises 3–4

3. Examine the figure, and answer the questions to determine whether or not the triangles shown are similar.
   a. What information is given about the triangles in Figure 3?
   b. How can the information provided be used to determine whether △ 𝐴𝐵𝐶 is similar to △ 𝐴𝐵′𝐶′?
   c. Compare the corresponding side lengths of △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′. What do you notice?
   d. Based on your work in parts (a)–(c), make a conjecture about the relationship between △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′.
   Explain your reasoning.
   
4. Examine the figure, and answer the questions to determine whether or not the triangles shown are similar.
   a. What information is given about the triangles in Figure 4?
   b. How can the information provided be used to determine whether △ 𝐴𝐵𝐶 is similar to △ 𝐴𝐵′𝐶′?
   c. Compare the corresponding side lengths of △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′. What do you notice?
   d. Based on your work in parts (a)–(c), make a conjecture about the relationship between △ 𝐴𝐵𝐶 and △ 𝐴𝐵′𝐶′. Explain your reasoning.

Exercises 5–10

5. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
   
6. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
   
7. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
   
8. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
   
9. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
   
10. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.9. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
    
11. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
    
12. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.
    
13. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement.

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