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Similar Triangles

Similar Triangles. same shape but different sizes. X. A. a. D ABC ~ D XYZ. a. c. c. b. b. B. C. Y. Z. All angles are equal. Sides are proportional. D. Similar triangles have the same shape. A. B. C. E. F. Similar Triangles.

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Similar Triangles

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  1. Similar Triangles same shape but different sizes X A a DABC ~ DXYZ a c c b b B C Y Z All angles are equal Sides are proportional

  2. D Similar triangles have the same shape. A B C E F Similar Triangles Similar triangles have corresponding angles equal and corresponding sides are proportional. If DABC ~ DDEF then ÐA = ÐD , ÐB = ÐE , ÐC = ÐF

  3. X Conditions for similarity A 1) SSS~ B C Y Z X A 2) SAS~ b b B C Y Z X A 3) AA~ c c b b B C Y Z

  4. Example: If DPQR ~ DSTU then ÐS ÐP = ÐT ÐQ = ÐU ÐR = Example: Show that DDEF ~ DXYZ D What is the scale factor? 4 2 X 6 F E 3 the scale factor is 1.5 Z Y

  5. Example: Show that DDEF ~ DXYZ D 60° ÐD = ÐX, ÐE = ÐY ÐF = ÐZ X 30° 90° 60° F E 90° 30° Z Y \DDEF ~ DXYZ

  6. Example: Show that DABC ~ DPQR P A 4 6 3 2 B C 5 Q R 7.5 \DABC ~ DPQR What is the scale factor? Ans: 1.5

  7. Are the triangles similar? Yes by AA

  8. Are the triangles similar? yes by AA

  9. Are the triangles similar? 4 6 3 4.5 yes by SAS~

  10. The following triangles are similar, calculate the values of x and y. 15 12 x 14 8 y

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