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Similar Triangles

Similar Triangles. Sydni Jordan - Olivia Smith Warren Mott High School 9B. rade evel ontent xpectation. L. C. E. G. G. G eometry TR. Transformations and Symmetry 07. Grade 7 05 5 th Expectation. MMSTC. 2. G.TR.07.05. Show that two triangles are similar using:

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Similar Triangles

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  1. Similar Triangles Sydni Jordan - Olivia Smith Warren Mott High School 9B

  2. rade evel ontent xpectation L C E G G.Geometry TR. Transformations and Symmetry 07. Grade 7 05 5th Expectation MMSTC 2

  3. G.TR.07.05 Show that two triangles are similar using: AA similarity SAS similarity SSS similarity Use these criteria to solve problems and to justify arguments. MMSTC 3

  4. Terms to Know Similar:Whenever two or more objects have proportional sides and congruent angles SSS: Way of proving triangles are similar when they have 3 pairs of proportional sides SAS: Way proving triangles are similar using two pairs of proportional sides and one pair of congruent angles AA: A way to prove triangles are similar when they have two pairs of congruent angles Congruent: When objects have the exact same size/shape Corresponding: having the same relationship 5 in. 5 in. 5 in. 5 in. 2 in. 2in . 5 in. 2 in. MMSTC 4

  5. Proportionality When corresponding sides of a triangle have the same ratio 6 cm 3 cm 4 cm 8 cm MMSTC 5

  6. AA Angle–Angle Similarity Corresponding angles must be congruent MMSTC 6

  7. AA Similarity MMSTC 7

  8. SAS Side-Angle-Side similarity Sides have to be proportional and corresponding angles have to be congruent MMSTC 9

  9. SAS 2 in 2 in. 3 in 3 in MMSTC 10

  10. 3 in.

  11. SSS Side-Side-Side Similarity Corresponding sides must be proportional MMSTC 12

  12. SSS 10 in. 8 in. 5 in. 4 in. 6 in. 3 in. MMSTC 13

  13. What Not To Use Wrong methods to use ASA SSA AAS

  14. Review Proportionality AA 6 cm 3 cm 4 cm 8 cm MMSTC MMSTC

  15. Review SAS SSS 10 in. 5 in. 8 in. 4 in. 3 in. 6 in.

  16. Resources • B, Christian. "Applying Similar Triangles to the Real World." similartraiangles3. PBWorks, 2010. Web. 28 Feb 2012. <http://similartriangles3.pbworks.com/w/page/23053498/Applying Similar Triangles to the Real World>. • Michigan. Michigan Department of Education. Mathematics Alignment At A Glace. Michigan: Michigan, Web. <http://www.michigan.gov/documents/alignment_at_a_glance-7thweb_134801_7.doc>. MMSTC 17

  17. Any Questions? MMSTC 18

  18. Now time for... THE QUIZ!

  19. Choose a Box! 1 2 3 4 5 6

  20. Are these triangles similar? Yes 10 cm 10 cm 4 cm No 7 cm 4 cm 7 cm Return

  21. For these triangles to be similar, what must the length of the missing segment be? 1.5 in. 2.5 in. ? 5 in. 4 in. 2 in. 10 in. 8 in. 3.5 in. Return

  22. Which method can be used to find out if these two triangles are similar? AA 60º SSS 3 cm 2 cm SAS 75º 45º 75º Return

  23. If you have two pairs of congruent angles in two triangles, which similarity can be used to prove that they are similar? SSS SAS AA Return

  24. Are these triangles similar? YES 45º 45º 8 in. 4 in. NO 7 in. 3.5 in. Return

  25. Which one is not a way to prove that triangles are similar? AA SSA SAS Return

  26. CORRECT!

  27. INCORRECT!

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