advertisement

Name _______________________________________ Date __________________ Class __________________ LESSON 7-3 Reteach Triangle Similarity: AA, SSS, and SAS Angle-Angle (AA) Similarity Side-Side-Side (SSS) Similarity Side-Angle-Side (SAS) Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar. ABC DEF ABC DEF ABC DEF Explain how you know the triangles are similar, and write a similarity statement. 1. 2. ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ 3. Verify that ABC MNP. ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 7-22 Holt Geometry Name _______________________________________ Date __________________ Class __________________ LESSON 7-3 Reteach Triangle Similarity: AA, SSS, and SAS continued You can use AA Similarity, SSS Similarity, and SAS Similarity to solve problems. First, prove that the triangles are similar. Then use the properties of similarity to find missing measures. Explain why ADE ABC and then find BC. Step 1 Prove that the triangles are similar. A A by the Reflexive Property of . AD 3 1 AB 6 2 AE 2 1 AC 4 2 Therefore, ADE ABC by SAS . Step 2 Find BC. AD DE AB BC 3 3.5 6 BC Corresponding sides are proportional. Substitute 3 for AD, 6 for AB, and 3.5 for DE. 3(BC) 6(3.5) Cross Products Property 3(BC) 21 Simplify. BC 7 Divide both sides by 3. Explain why the triangles are similar and then find each length. 4. GK 5. US ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 7-23 Holt Geometry Name _______________________________________ Date __________________ Class __________________ LESSON 7-3 Reading Strategies Use a Graphic Aid Use the flowchart to determine, if possible, whether the following pairs of triangles are similar. If similar, write AA , SSS , or SAS —the postulate or theorem you used to conclude that they are similar. If it is not possible to conclude that they are similar, write no conclusion. 1. 2. ________________________________________ 3. ________________________________________ 4. ________________________________________ 5. ________________________________________ 6. ________________________________________ 7. ________________________________________ 8. ________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 7-26 Holt Geometry Name _______________________________________ Date __________________ Class __________________ LESSON 7-3 Practice B Triangle Similarity: AA, SSS, SAS For Exercises 1 and 2, explain why the triangles are similar and write a similarity statement. 1. 2. ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ For Exercises 3 and 4, verify that the triangles are similar. Explain why. 3. JLK and JMN 4. PQR and UTS ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ For Exercise 5, explain why the triangles are similar and find the stated length. 5. DE ________________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 7-20 Holt Geometry Name _______________________________________ Date __________________ Class __________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 7-20 Holt Geometry