Q3-W6.1 - Triangle Similarity Theorem ( SAS,SSS,AA).pptx

This presentation is for grade 9

1. Pulo National High School WELCOME to MATHEMATICS 9 CLASS ! Gina Acayen -Trinidad Teacher

2. LESSON TITLE : Triangle Similarity Theorem

3. At the end of the lesson, learners are expected to: Prove the conditions for similarity of triangles. 1.1 AA Similarity Theorem 1.2 SSS Similarity Theorem 1.3 SAS Similarity Theorem (M9GE-IIIg-h-1) Objectives:

4. In this lesson, we are only going to focus on the similarity of two triangles . We will apply our prior knowledge on the definition of similar polygons to understand the postulates and theorems in proving the similarity of triangles. Triangle Similarity Theorems To prove the similarity of two triangles using the definition of similarity, we must establish that the three corresponding angles are congruent and that the three ratios of the lengths of corresponding sides are equal .

5. AAA Similarity Postulate If the three angles of one triangle are congruent to the three angles of another triangle, then the two triangles are similar

6. Quiz on AAA Similarity Postulate Do this! Pages 368 – 369

7. Here are the other Triangle Similarity Theorems:

8. 1.) AA Similarity Theorem If two angles of one triangle are congruent respectively to two angles of another triangle, then the triangles are similar. Illustration Given: ∠A ≅∠O ; ∠C ≅∠D Prove: △CAT ∼△DOG C

9. Proof:

10. Quiz on AA Similarity Theorem Do this! Pages 370-371

11. 2.) SSS Similarity Theorem If the three corresponding sides of two triangles are proportional, then the two triangles are similar Illustration Given: △ARM ⟷ △LEG, , Prove: △ARM ∼ △LEG  

12. Proof:

13. Quiz on SSS Similarity Theorem Do this! Page 373

14. 3.) SAS Similarity Theorem If an angle of one triangle is congruent to an angle of another triangle and if the lengths of the sides including these angles are proportional, then the triangles are similar. Illustration Given: △XYZ ⟷ △ABC, ∠Y ≅ ∠B and Prove: △XYZ ∼ △ABC  

15. Proof:

16. Quiz on SAS Similarity Theorem Do this! Pages 375 – 376