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Okay, now without further adieu, get out notes for 7.3

Okay, now without further adieu, get out notes for 7.3. 7.3 Notes. The AAA Similarity Theorem: Concerning two triangles, if the corresponding angles are congruent, then the triangles are similar.

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Okay, now without further adieu, get out notes for 7.3

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  1. Okay, now without further adieu, get out notes for 7.3

  2. 7.3 Notes The AAA Similarity Theorem: Concerning two triangles, if the corresponding angles are congruent, then the triangles are similar.

  3. This is very handy. Before, we needed all angles to be congruent and all the sides to be proportional for two shapes to be similar.

  4. But now let’s think. Do we really need all three angles?

  5. hmmmmmmmmm . . .

  6. I’m still thinking . . .

  7. Wait a minute. If we had two corresponding angles congruent between triangles, wouldn’t the third have to be congruent? Heck yes it does Mr. Klos, you are soooooooo smart

  8. In other words . . .Instead of AAA, we only need AA to prove that triangles are similar. Mr. Klos, you are a genius!!! By the way, I don’t mean the support group.

  9. Dare I say . . . Sweet Sassy Molassy You are a bold man!!!

  10. Now this next setup is pretty intriguing . . .

  11. Take any right triangle . . .

  12. Draw an altitude . . .

  13. There are automatically three similar triangles . . .

  14. First, there is a big one . . .

  15. Then a medium one . . .

  16. And don’t forget that baby one . . . The secret is they all have a right angle and share an angle.

  17. So, let’s recap . . . how can we prove that triangles are similar?? AA

  18. When we conclude 7.3, you will have three total ways to prove that triangles are similar. That’s the point of today. The good news is that they will seem familiar.

  19. Oh, and by the way, I’m just talking about shortcuts to prove that TRIANGLES are similar. Any other shape has to have all angles congruent and all sides proportional

  20. The 2 other ways to prove that triangles are similar besides AA, is . . . SAS SSS

  21. When you see an A, it means the angle needs to be congruent. When you see an S, the sides don’t have to be congruent . . . Instead it’s that “p” word . . . Proportional

  22. The SAS Similarity: 8 8 ? 4 4 = 105° 105° 12 12 6 6 Yes, ergo the triangles are similar by SAS. Are the sides proportional???

  23. The SSS Similarity . . . If one triangle has sides of 12, 24, and 18 and another triangle has lengths of 4, 2, and 3 are the triangles similar? Only if the sides are proportional . . .

  24. Also, you have to give it a chance. The biggest sides must match up with each other, the same with the smallest and so forth. So, now back to that problem. . .

  25. If one triangle has sides of 12, 24, and 18 and another triangle has lengths of 4, 2, and 3 are the triangles similar? 2 ? 3 ? 4 = = 18 24 12 Since all the ratios reduce to 1/6, then the triangles are similar by SSS. Notice how I arranged them from smallest to largest??

  26. Practice this problem: One triangle has sides of 10, 8, and 6. Another has lengths of 9, 15, and 12. Are the triangles similar? Seriously, do the problem. Do you think you have the answer? Yes, they truly are similar.

  27. Find the value of x that makes L If the sides are proportional, we have an SAS. But which side goes with which? From above, LA and SA are in the same position, they go together. M 5x+7 4 A x x+2 C S

  28. Find the value of x that makes L M 5x+7 4 5x+7 x+2 A = x 4 x x+2 C S Cross multiply and solve from there. Check to see that x = 1.

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