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Do the triangles have the same shape?

Do the triangles have the same shape?. F. C. 60º. 60º. 24 cm. 16 cm. 14 cm. 21 cm. 40º. 80º. A. B. 80º. 10 cm. 40º. D. E. 15 cm. What do you notice about the lengths of the sides?. The sides are in the same ratio. A. Construct D ABC. Ð B = 50º. Ð C = 60º. 60º. 50º.

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Do the triangles have the same shape?

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  1. Do the triangles have the same shape? F C 60º 60º 24 cm 16 cm 14 cm 21 cm 40º 80º A B 80º 10 cm 40º D E 15 cm What do you notice about the lengths of the sides? The sides are in the same ratio.

  2. A Construct DABC ÐB = 50º ÐC = 60º 60º 50º BC = 4 cm C B 4 cm P Construct DPQR ÐQ = 50º 4 cm ÐR = 60º PQ = 4 cm 50º 60º R Q Are they identical? No

  3. Congruent Triangles: A X a a c c b b Z C B Y DABC @DXYZ ÐA = Ð AB = ÐB = Ð AC = ÐC = Ð BC =

  4. Conditions for congruence A X 1) B C Y Z A X 2) b b B C Y Z A X 3) c c b b B C Y Z

  5. Similar Triangles X A a DABC ~ DXYZ a c c b b B C Y Z All angles are equal Sides are proportional

  6. X Conditions for similarity A 1) B C Y Z X A 2) b b B C Y Z X A 3) c c b b B C Y Z

  7. 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 Z Y

  8. Example: Show that DDEF ~ DXYZ D ÐD = Ð ÐE = Ð ÐF = Ð X 30° 90° 60° F E 90° Z Y \DDEF ~ D

  9. 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?

  10. Are the triangles similar?

  11. Are the triangles similar?

  12. Are the triangles similar? 4 6 3 4.5

  13. Calculate the values of x and y. 15 12 x 14 8 y

  14. A tree is 3 m tall and casts a shadow of 2 m. A building casts a shadow of 12 m. Determine the height of the building. x 3 m 2 m 12 m The building is x =

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