1. Geometry 7.3 Similar Polygons

2. Similar Figures This is the same figure scaled differently. Each of the figures is proportional to the other two. ~ The symbol for SIMILAR is ~

3. Similar vs. Congruent The word similar has a specific meaning in Geometry. Congruent figures have: the same shape the same size Similar figures have: the same shape can be different sizes

4. Similar Polygons Their vertices can be paired so that: Corresponding angles are congruent Corresponding sides are in proportion (their lengths have the same ratio) 4 8 6 12 8 4 3 6

5. Order is important A B C DE M N O PQ ABCDE ~ MNOPQ m<A = m<M m<B = m<N m<C = m<O m<D = m<P m<E = m<Q

6. Are the polygons similar? Why or why not? No. Congruent angles, but sides not proportional 80 105 No. Proportional sides (they are the same), but angles are not congruent

7. Are the polygons similar? Why or why not? Yes. Congruent angles and proportional sides 40 50 4 3 5 6 8 10

8. Sometimes, Always, Never Similar  Two rectangles: ______  Two scalene triangles: _____  Two equilateral triangles: ______  Two rhombuses: _____  A right triangle and isosceles triangle: ______  A square and a rhombus: ___

9. ABCDEFA’B’C’D’E’F’ABCDEF ~ A’B’C’D’E’F’ Find the following: a. Scale Factor: ________ b. The values of v, x, y, z: c. Perimeters of two hexagons: d. Ratio of the perimeters: A BC D E F A’ B’C’ D’ E’F’ ABCDEF ~ A’B’C’D’E’F’ 30 12 y 15 z 20 8 6 x v 18

10. A B C D A’ B’ C’ D’ ABCD ~ A’B’C’D’ y 30 22 50 x 12 z 30  Scale factor: ________  Values of x, y, z : ________  The ratio of the perimeters: ________

11. Homework pg. 250 CE #1-10 WE #1-27 Makeups tomorrow after school Quiz Thursday

12. 130 60 Find m<B, m<Y, m<D and m<Z. AB C D W X Y Z m <B = m <X = 60 m <Y = m <C = 130 m <A = m< W = 90 m < D = 360 – (90 + 60 + 130) m < D = 360 – 280 m < D = 80 = m < Z 60 130 EXAMPLE:

13. Scale Factor If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Scale factor is 2 4 6 12 1313 == 1313

14. Quad ABCD ~ Quad A’B’C’D’ (read A prime, B prime, etc.) Find the: (a)scale factor (b) values of x, y and z (c)perimeters of the two quadrilaterals (d)ratio of the perimeters 10 20 8 x z 30 21 y D D’ C C’ B B’ A A’

15. 10 20 8 x z 30 21 y D D’ C C’ B B’ A A’ Scale factor: DC D’C’ = 20 30 = 2 3 2 3 = x 21 x = 14 2 3 = 8 y y = 12 2 3 = 10 z z = 15

16. 10 20 8 14 15 30 21 12 D D’ C C’ B B’ A A’ Perimeter of quad ABCD is 10 + 20 + 8 + 14 = 52 Perimeter of quad A’B’C’D’ is 15 + 30 + 12 + 21 = 78 Ratio of perimeters is 52 78 = 2 3

17. From the homework pg. 250 #1-4 pg. 251 #26