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Chapter 8 Lesson 3

Chapter 8 Lesson 3. Objective: To use AA, SAS and SSS similarity statements. Postulate 8-1   Angle-Angle Similarity (AA ~) Postulate

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Chapter 8 Lesson 3

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  1. Chapter 8 Lesson 3 Objective: To use AA, SAS and SSS similarity statements.

  2. Postulate 8-1   Angle-Angle Similarity (AA ~) Postulate                                                                                    If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. ∆TRS ~ ∆PLM

  3. Example 1: Using the AA~ Postulate Explain why the triangles are similar. Write a similarity statement. RSWVSB because vertical angles are congruent.  RV because their measures are equal. ∆RSW ~ ∆VSB by the Angle-Angle Similarity Postulate.

  4. M K 58° 58° B A X Example 2: Using the AA~ Postulate Explain why the triangles are similar. Write a similarity statement. ∆AMX~∆BKX by AA~ Postulate

  5. Theorem 8-1   Side-Angle-Side Similarity (SAS ~) Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar. Theorem 8-2   Side-Side-Side Similarity (SSS ~) Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar.

  6. Example 3: Using Similarity Theorems                                                                                     Explain why the triangles must be similar. Write a similarity statement. QRPXYZ because they are right angles. Therefore, ∆QRP ~ ∆XYZ by the SAS ~ Theorem

  7. Example 4: Using Similarity Theorems Explain why the triangles must be similar. Write a similarity statement.                  ∆ABC ~ ∆EFG by SSS~ Theorem

  8. Example 5: Finding Lengths in Similar Triangles  Explain why the triangles are similar. Write a similarity statement. Then find DE. Because vertical angles are congruent. ΔABC ~ ΔEBD by the SAS~ Theorem.

  9. Example 6: Finding Lengths in Similar Triangles Find the value of x in the figure.

  10. Indirect Measurement is when you use similar triangles and measurements to find distances that are difficult to measure directly.

  11. Example 7: Indirect Measurement Geology Ramon places a mirror on the ground 40.5 ft from the base of a geyser. He walks backwards until he can see the top of the geyser in the middle of the mirror. At that point, Ramon's eyes are 6 ft above the ground and he is 7 ft from the image in the mirror. Use similar triangles to find the height of the geyser. ∆HTV ~ ∆JSV The geyser is about 35 ft. high.

  12. Example 8: Indirect Measurement In sunlight, a cactus casts a 9-ft shadow. At the same time a person 6 ft tall casts a 4-ft shadow. Use similar triangles to find the height of the cactus. X 6 4 9

  13. Assignment

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