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5.2 Investigating and Comparing Triangles

5.2 Investigating and Comparing Triangles. Part 1: Are 3 sides enough?. C. Construct D ABC. 5 cm. 6 cm. AB = 3 cm. BC = 6 cm. Z. AC = 5 cm. A. B. 3 cm. 2 sides ?. Construct D XYZ. 6 cm. 6 cm. 6 cm. 6 cm. XY = 3 cm. YZ = 6 cm. 3 cm. Y. X.

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5.2 Investigating and Comparing Triangles

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  1. 5.2 Investigating and Comparing Triangles Part 1: Are 3 sides enough? C Construct DABC 5 cm 6 cm AB = 3 cm BC = 6 cm Z AC = 5 cm A B 3 cm 2 sides ? Construct DXYZ 6 cm 6 cm 6 cm 6 cm XY = 3 cm YZ = 6 cm 3 cm Y X

  2. 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.

  3. Part 2:Are two sides enough? C Construct DABC C 5 cm 5 cm AB = 7 cm AC = 5 cm A 7 cm B Assume ÐA = 40º C Construct DABC 5 cm AB = 7 cm 40º AC = 5 cm B A 7 cm ÐA = 40º

  4. C 5 cm 40º B A 7 cm F Construct DDEF 5 cm DE = 7 cm 40º DF = 5 cm E D 7 cm ÐE = 40º F 5 cm 40º D E 7 cm

  5. Part 3:Are two angles enough? A Construct DABC ÐB = 50º ÐC = 60º 50º 60º B C A 60º 50º C B

  6. 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

  7. Congruent Triangles: identical in every way same size and same shape A X a a c c b b Z C B Y DABC @DXYZ ÐA = ÐX AB = XY ÐB = ÐY AC = XZ ÐC = ÐZ BC = YZ

  8. Conditions for congruence A X 1) SSS B C Y Z A X 2) SAS b b B C Y Z A X 3) ASA c c b b B C Y Z

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Are the triangles similar? Yes by AA

  15. Are the triangles similar? yes by AA

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

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

  18. 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 18 m tall. x =18 m

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