Similar Triangles 8.3

1. Similar Triangles 8.3

2. homework • Identify similar triangles. • Learn the definition of AA, SAS, SSS similarity. • Use similar triangles to solve problems.

3. homework

4. homework

5. homework Explain why the triangles are similar and write a similarity statement. BCA  ECD by the Vertical Angles Theorem. Also, A  D by the Right Angle Congruence Theorem. Therefore ∆ABC ~ ∆DEC by AA Similarity.

6. homework Explain why the triangles are similar and write a similarity statement. D  H by the Definition of Congruent Angles. Arrange the sides by length so they correspond. Therefore ∆DEF ~ ∆HJK by SAS Similarity.

7. homework Explain why the triangles are similar and write a similarity statement. Arrange the sides by length so they correspond. Therefore ∆PQR ~ ∆STU by SSS similarity.

8. homework Explain why the triangles are similar and write a similarity statement. TXU VXW by the Vertical Angles Theorem. Arrange the sides by length so they correspond. Therefore ∆TXU ~ ∆VXW by SAS similarity.

9. homework Explain why the triangles are similar and write a similarity statement. By the Triangle Sum Theorem, mC = 47°, so C F. B E by the Right Angle Congruence Theorem. Therefore, ∆ABC ~ ∆DEF by AA Similarity.

10. homework Determine if the triangles are similar, if so write a similarity statement. By the Definition of Isosceles, A C and P R. By the Triangle Sum Theorem, mB = 40°, mC = 70°, mP = 70°, andmR = 70°. Therefore, ∆ABC ~ ∆DEF by AA Similarity.

11. homework Explain why ∆ABE ~ ∆ACD, and then find CD. Prove triangles are similar. A A by Reflexive Property, and B C since they are right angles. Therefore ∆ABE ~ ∆ACD by AA similarity. x(9) = 5(12) 9x = 60

12. homework Explain why ∆RSV ~ ∆RTU and then find RT. Prove triangles are similar. It is given that S T. R R by Reflexive Property. Therefore ∆RSV ~ ∆RTU by AA similarity. RT(8) = 10(12) 8RT = 120 RT = 15

13. Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons, Given RS || UT, RS = 4, RQ = x + 3, QT= 2x + 10, UT = 10, find RQ and QT. RQ = 8; QT = 20

14. 100 35 45 homework Determine if the triangles are similar, if so write a similarity statement. Find the missing angles. Check for proportional sides. AA Similar AEZ ~ REB SAS Similar AGU ~ BEF Check for proportional sides. Check for proportional sides. SSS Similar ABC ~ FED Not Similar

15. Vertical angles. Alternate Interior angles. 120 45 Find the missing angles. homework Determine if the triangles are similar, if so write a similarity statement. Check for proportional sides. Sides do not correspond. AA Similar FGH ~ KJH Not Similar. Not Similar. Check for proportional sides. Check for proportional sides. Not Similar. Not Similar. Not Similar.

16. homework Given ABC~EDC, AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC and CE. • A • B • C • D CE = x + 2 AC = 3x + 8 AC = 2 + 2 AC = 3(2) + 8 AC = 14 AC = 4

17. homework Each pair of triangles below are similar, find x.

18. homework

19. homework

20. Assignment Section 11 – 36