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Warm-Up

Warm-Up. Q. K. ∆KLM ~ ∆PQR 1) Find the scale factor. 2) Find the length of segment PQ. 3) Find the measure of angle Q. 4) The ratio of width to length for a garden is 2:5. The perimeter is 126 ft. Find the values of the width and length. P. 8. 105 °. 15. 45 °. L. M. 10. R.

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Warm-Up

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  1. Warm-Up Q K • ∆KLM ~ ∆PQR • 1) Find the scale factor. • 2) Find the length of segment PQ. • 3) Find the measure of angle Q. • 4) The ratio of width to length for a garden is 2:5. The perimeter is 126 ft. Find the values of the width and length. P 8 105° 15 45° L M 10 R

  2. Homework ?s

  3. Quiz

  4. 8.4 Similar Triangles

  5. Similar Triangles • In the diagram, ∆BTW ~ ∆ETC. • Write the statement of proportionality. • Find m∠TEC. • Find ET and BE. T 34° E C 3 20 79° B W 12

  6. 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. A E C B G F

  7. Additional Theorems • Side-Side-Side (SSS) Similarity • If corresponding sides are proportional, the triangles are similar • Just as we discussed with all polygons • If • Then ∆ABC ~ ∆EFG A E C B G F

  8. Additional Theorems • Side-Angle-Side (SAS) Similarity • Within two triangles, if two sets of corresponding sides are proportional and the included angles are equal, then the triangles are similar • If and m∠B≅m∠F, • Then ∆ABC ~ ∆EFG A E C B G F

  9. Similar Triangles • Given the triangles are similar, find the value of the variable. )) m )) ) 6 8 11m = 48 ) 11

  10. 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

  11. ∆ABC ≈ ∆DBE. • Solve for the variables. A 5 D y 9 x B C E 8 4

  12. 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.

  13. 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.

  14. Determine which two of the three given triangles are similar. Find the scale factor for the pair. K N R 6 9 6 4 6 10 Q M S P 14 8 L J 12

  15. The 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

  16. 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

  17. Practice (22 problems) • P. 484 #18-26, 39-44 • P. 492 #6-12

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