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Proving Triangles Similar through SSS and SAS

Proving Triangles Similar through SSS and SAS. CH 6.5. Side Side Side Similarity Theorem. If the corresponding side lengths of 2 triangles are proportional, then the triangles are similar. To prove 2 triangles similar using SSS.

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Proving Triangles Similar through SSS and SAS

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  1. Proving Triangles Similar through SSS and SAS CH 6.5

  2. Side SideSide Similarity Theorem • If the corresponding side lengths of 2 triangles are proportional, then the triangles are similar

  3. To prove 2 triangles similar using SSS • In order to prove similarity using SSS, you must check each possible proportion of the side lengths of a triangle. Not similar

  4. Use SSS to find the Scale Factor and determine whether the triangles are similar…if they are similar name the triangles correctly ∆ ABC ~∆DEF

  5. Use SSS to find the Scale Factor and determine whether the triangles are similar Not Similar

  6. Assuming that ∆ ABC~ ∆ DEFfind x.Each proportion will equal the scale factor 4(3x+3) = 8(12) 12x + 12 = 96 = x = 7 12x = 84

  7. Assuming that ∆ XYZ~ ∆ PQRfind x.Each proportion will equal the scale factor 3(12) = 2(3x -6) 36 = 6x -12 x = 8 48 = 6x

  8. Side Angle Side Similarity Theorem • If 2 triangles have a corresponding congruent angle and the sides including that angle are proportional, then the 2 triangles are similar.

  9. Are the Triangles similar?How? yes SAS Name the corresponding Side, Angle, and Side for each triangle

  10. Are the Triangles similar?How? yes SAS Name the corresponding Side, Angle, and Side for each triangle Find the scale factor to back it up

  11. Are the Triangles similar?How? yes SAS or SSS Name the corresponding Side, Angle, and Side and Side, Side, Side for each triangle. Find the scale factor to back it up

  12. Find the Scale Factor and determine whether the triangles are similar using SAS ∆ RST ~ ∆ XYZ

  13. Is there enough information to determine whether the triangles are similar? no Why? The sides are not proportional and it does not follow SAS.

  14. Is there enough information to determine whether the triangles are similar? yes Which Similarity Postulate allows us to say yes? SAS

  15. Are the triangles similar? Which similarity postulate allows us to say it is similar? yes SAS The sides are proportional and the included angles are congruent.

  16. Are the triangles similar? Which similarity postulate allows us to say it is similar? yes SAS 2 sides are proportional and the included angle is congruent.

  17. Assuming that these triangles are similar. Let’s solve for the missing variables. 3x + 8 13y - 38 12 4x - 5 15 6y + 11

  18. Page 391 • #3- 9, 15 - 23

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