PARTS OF SIMILAR TRIANGLES

1. PARTS OF SIMILAR TRIANGLES • Recognize and use proportional relationships of corresponding perimeters of similar triangles. • Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. JOHN B. CORLEY

2. PROPORTIONAL PERIMETERS THEOREM If two triangles are similar, then the perimeters are proportional to the corresponding sides. JOHN B. CORLEY

3. Example 1– Perimeters of Similar Triangles If ∆LMN ~ ∆QRS, QR = 35, RS = 37, SQ = 12, and NL = 5, find the perimeter of ∆LMN N 5 M L S 37 12 R Q 35 JOHN B. CORLEY

4. Example 1– Perimeters of Similar Triangles, cont. Let x represent the perimeter of ∆LMN. The perimeter of ∆QRS = 35 + 37 + 12 or 84. 5 Perimeter = 84 37 12 35 JOHN B. CORLEY

5. Example 1– Perimeters of Similar Triangles, cont. Let x represent the perimeter of ∆LMN. The perimeter of ∆QRS = 35 + 37 + 12 or 84. 5 Perimeter = 84 37 12 35 JOHN B. CORLEY

6. SPECIAL SEGMENTS OF SIMILAR TRIANGLES Corresponding Altitudes U Q T W V A P R JOHN B. CORLEY

7. SPECIAL SEGMENTS OF SIMILAR TRIANGLES Corresponding Angle Bisectors U Q T X P B R JOHN B. CORLEY

8. SPECIAL SEGMENTS OF SIMILAR TRIANGLES Corresponding Medians U Q T V Y P M R JOHN B. CORLEY

9. Example 2– Medians of Similar Triangles ∆ABC ~ ∆DEF BG and EH are medians BC = 30, BG = 15, EF = 15 Find EH B 30 15 A C G E 15 x D F H JOHN B. CORLEY

10. Example 2– Medians of Similar Triangles ∆ABC ~ ∆DEF BG and EH are medians BC = 30, BG = 15, EF = 15 Find EH B 30 15 A C G E 15 x D F H JOHN B. CORLEY

11. Example 3– Solve Problems with Similar Triangles PHOTOGRAPHY 6.16 m 42 mm x 35 mm JOHN B. CORLEY

12. ANGLE BISECTOR THEOREM An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. Q P B R JOHN B. CORLEY