1. Warm-up Proportions WS Can you solve for x AND Y? 2 = X = 10 312 Y

2. Similar Polygons

3. Identifying Similar Polygons Definition: Similar Polygons Two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons.

4. Similar polygons If ABCD ~ EFGH, Similarity Statement Proportionality Statement then A B C D E F G H

5. Similar polygons Given ABCD ~ EFGH, solve for x. A B C D E F GH 2 4 6 x 2x = 24 x = 12

6. Is ABC ~ DEF? Explain. A B C D E F 10 12 13 5 6 7 ?? yes no ABC is not similar to DEF since corresponding sides are not proportional.

7. Similar polygons Given ABCD ~ EFGH, solve for the variables. A B C D E F GH 2 6 5 x 10 y

8. If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Ex: Scale factor of this triangle is 1:2 3 6 9 4.5

9. Quadrilateral JKLM is similar to PQRS. Find the value of z. Also find the scale factor. J KL M P Q R S 10 15 z 6 15z = 60 z = 4

10. Similar Triangles

11. In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. Find m<TEC. Find ET and BE. T EC WB 3 12 20 34° 79°

12. 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.

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

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

15. ∆ABC ≈ ∆DBE. 9 48 5 x y B A C D E