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7.3 Similar Triangles

7.3 Similar Triangles. Spi.4.11 Use basic theorems about similar and congruent triangles to solve problems. Check.4.36 Use several methods, including AA, SSS, and SAS, to prove that two triangles are similar.

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7.3 Similar Triangles

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  1. 7.3 Similar Triangles Spi.4.11 Use basic theorems about similar and congruent triangles to solve problems. Check.4.36 Use several methods, including AA, SSS, and SAS, to prove that two triangles are similar. CLE 3108.4.8 Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations.

  2. ""Thunder is good, thunder is impressive; but it is lightning that does the work." Mark Twain Triangle Similarity Q S R P T U Q S a c ax cx R b P U T bx Q S a c cx ax R P U T

  3. Determine if triangles are similar In the figure, FGEG, BE=15, CF=20, AE=9 and DF=12. Determine which triangles are similar. C FGE is an isosceles triangle so GFE  GEF If you can show AE & BE proportional to DF and CF, then SAS Similarity to show triangles as similar B G A D E F Two are proportional So ABE  DCF

  4. Determine if triangles are similar In the figure, AB||DC, BE=27, DE = 45, AE = 21, CE=35. Determine which two triangles are similar CDE EBA because they are alternate interior angles BEA CED, because they are vertical angles C ABE  CDE, because AA Similarity Check B D E A

  5. Find parts of similar Triangles C A x -1 E 5 • Find AE and DE 2 Since AB|| CD B ABEDCE and BAECDE because alternate interior angles x + 5 D ABE~DCE because of AA similarity ABE~DCE because of AA similarity EA = x – 1 = 5 – 1 = 4 2(x+5) = 5(x – 1) 2x + 10 = 5x – 5 15 = 3x 5 = x DE = x + 5 = 5 + 4 = 9

  6. Indirect measurements 0.9 x = 1.2(240) 0.9x = 288 x = 288/.9=320

  7. 2 x = 12(242) 2x = 2904 x = 1452 Actual height 1450

  8. Practice Assignment • Page 479, 10 – 24 even • Notebook Check and Quiz Tomorrow

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