Geometry 7.3 Similar Polygons

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

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

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

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

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

Are the polygons similar? Why or why not? Yes. Congruent angles and proportional sides

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: ___

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’ y 15 z x v 18

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

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

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 – ( ) m < D = 360 – 280 m < D = 80 = m < Z EXAMPLE:

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 == 1313

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 x z y D D’ C C’ B B’ A A’

x z y D D’ C C’ B B’ A A’ Scale factor: DC D’C’ = = = x 21 x = = 8 y y = = 10 z z = 15

D D’ C C’ B B’ A A’ Perimeter of quad ABCD is = 52 Perimeter of quad A’B’C’D’ is = 78 Ratio of perimeters is = 2 3

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