1 / 13

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

terentia-avis
Télécharger la présentation

Chapter 8 Lesson 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related