7.3 Similar Triangles

Objectives/Assignment Identify similar triangles. Use similar triangles to solve problems

Identifying Similar Triangles In this lesson, you will continue the study of similar polygons by looking at the properties of similar triangles.

Ex. 1: Writing Proportionality Statements Given, ∆BTW ~ ∆ETC. Write the statement of proportionality. Find m  TEC. Find ET Find BE. 34° 79°

Ex. 1: Writing Proportionality Statements In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. 34° ET TC CE = = BT TW WB 79°

Ex. 1: Writing Proportionality Statements In the diagram, ∆BTW ~ ∆ETC. Find m  TEC. B  TEC, SO m  TEC = 79° 34° 79°

Ex. 1: Writing Proportionality Statements In the diagram, ∆BTW ~ ∆ETC. Find ET and BE. 34° CE ET Write proportion. = WB BT 3 ET Substitute values. = 12 20 3(20) ET Multiply each side by 20. = 79° 12 5 = ET Simplify. Because BE = BT – ET, BE = 20 – 5 = 15. So, ET is 5 units and BE is 15 units.

Angle-Angle Similarity Postulate

Notes Solution:

Notes

Notes

Take Notes: Solution: 12x = 60 x = 5 12y = 40 y = 3.3

Take Notes: Solution: 6x = 30 x = 5 3y + 15 = 24 y = 3

Take Notes: Solution: 15x = 240 x = 16 39y = 780 y = 20

Proofs:

Proofs:

Practice: Solution: 9x = 72 x = 8

Practice: Solution: 16x = 36 * 20 16x = 720 x = 45

Practice: Solution: 32x = 800 x = 25

Practice: Solution: 12x = 48 x = 4

Practice: Solution: 5x - 5 = 30 5 x = 35 x = 7

Practice: Solution: 8x - 16 = 40 8 x = 56 x = 7

Practice: Solution: 16x - 8 = 56 16 x = 64 x = 4

Practice: Solution: 4x - 8 = 12 4 x = 20 x = 5