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Understanding Triangle Similarity by Angle-Angle Criterion

Learn how two triangles can be proven similar using the Angle-Angle postulate. Discover why only 2 congruent angles are needed for similarity, and explore the concept in depth.

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Understanding Triangle Similarity by Angle-Angle Criterion

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Presentation Transcript

  1. Prove Triangles Similar by AA 6.4

  2. Another Postulate All you need are any 2 congruent angles for 2 triangles to be similar.

  3. Why only 2 angles? • We know that the sum of the interior angles has to be 180. • Therefore, the third angle also has to be congruent.

  4. Are the 2 triangles similar? Why or why not? yes

  5. Are the 2 triangles similar? Why or why not? yes

  6. Are the 2 triangles similar? Why or why not? yes

  7. Are the 2 triangles similar? Why or why not? no

  8. Are the 2 triangles similar? Why or why not? no

  9. Are the 2 triangles similar? Why or why not? yes

  10. Are the 2 triangles similar? Why or why not? no

  11. Are the 2 triangles similar? Why or why not? yes

  12. Are the 2 triangles similar? Why or why not? Can’t tell

  13. Are the 2 triangles similar? Why or why not? Yes

  14. Are the 2 triangles similar? Why or why not? Yes

  15. Are the 2 triangles similar? Why or why not? Can’t tell

  16. Are the 2 triangles similar? Why or why not? yes

  17. Are the 2 triangles similar? Why or why not? yes

  18. Are the 2 triangles similar? Why or why not? yes

  19. Find the length of x, then find BD

  20. Find the length of x, then find BD

  21. Proportion Word Problems

  22. Molly wants to know the height of the flagpole in front of the town hall. She sees that it casts a shadow 24 ft long. She drives a stake into the ground beside the flagpole. The stake is 4 ft high with a shadow 2 feet long. How tall is the flagpole?

  23. The scale on a map says that 1 inch equals 150 miles. How many miles apart are two cities if you measure 4 ½ inches between them?

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