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8.4 Similar Triangles

8.4 Similar Triangles. In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. TE:TB as TC:TW as EC:BW Find m<TEC. <TEC Corresponds to <EBW; So <TEC = 79° Find ET and BE. TE = EC so.. x = 3 TB BW 20 12 12x = 60 x = 5. T. 34°. E. C. 3. 20.

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8.4 Similar Triangles

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  1. 8.4 Similar Triangles

  2. In the diagram, ∆BTW ~ ∆ETC. • Write the statement of proportionality. • TE:TB as TC:TW as EC:BW • Find m<TEC. • <TEC Corresponds to • <EBW; So <TEC = 79° • Find ET and BE. • TE = EC so.. x = 3 • TB BW 20 12 • 12x = 60 x = 5 T 34° E C 3 20 79° B W 12

  3. Postulate 25 • Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

  4. Similar Triangles • Given the triangles are similar. Find the value of the variable. )) m )) ) 6 8 11m = 48 ) 11

  5. Similar Triangles • Given the triangles are similar. Find the value of the variable. Left side of sm Δ Base of sm Δ Left side of lg Δ Base of lg Δ = 6 5 > 2 6h = 40 > h

  6. ∆ABC ≈ ∆DBE. A 5 D y 9 x B C E 8 4

  7. Determine whether the triangles are similar. 6 32° 33° 9 18 No, because two angles of one triangle are not congruent to two angles of another triangle.

  8. Determine whether the triangles are similar. 60° 60° 60° 60° Yes, because two angles of one triangle are congruent to two angles of another triangle.

  9. Given two triangles are similar, solve for the variables. 2b - 8 a + 3 14 15 16 ) ) 10 15(a+3) = 10(16) 15a + 45 = 160 15a = 115

  10. Decide whether two triangles are similar, not similar, or cannot be determined. A 92° 31° S 47° 41° 92° 57° S + 92 + 41 = 180 S + 133 = 180 S = 47 A + 92 + 57 = 180 A + 149 = 180 A = 31 Not similar

  11. Homeworkl • 8.4 p. 483-487 • 10-48E and 57

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