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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) 12 6 4 4 8 8 3 6 Order is important N B M A O C E D ABCDE ~ Q P MNOPQ m<A = m<M m<C = m<O m<B = m<N m<D = m<P m<E = m<Q Are the polygons similar? Why or why not? 105 80 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? 4 40 5 10 8 50 6 3 Yes. Congruent angles and proportional sides Sometimes, Always, Never Similar Two rectangles: ______ Two equilateral triangles: ______ A right triangle and isosceles triangle: ______ Two scalene triangles: _____ Two rhombuses: _____ 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: 18 F 20 E 8 F’ 30 E’ z 12 A D A’ D’ v 6 15 y B’ C’ B C x 12 ABCDEF ~ A’B’C’D’E’F’ 50 D C 22 30 Scale factor: ________ A 30 D’ x A’ Values of x, y, z : ________ The ratio of the perimeters: ________ B y 12 C’ z B’ ABCD ~ A’B’C’D’ Homework pg. 250 CE #1-10 WE #1-27 Makeups tomorrow after school Quiz Thursday EXAMPLE: Find m<B, m<Y, m<D and m<Z. C D Z 130 130 60 B Y 60 A W X m <B = m <X = 60 m < D = 360 – (90 + 60 + 130) m <Y = m <C = 130 m < D = 360 – 280 m <A = m< W = 90 m < D = 80 = m < Z Scale Factor • If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. 6 2 4 = = 1 3 12 Scale factor is 1 3 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 D’ D 20 C 10 A 30 z y 8 x B C’ A’ 21 B’ D’ D 20 x Scale factor: 3 = y 8 A 2 C’ z C 10 30 B DC D’C’ x 2 21 3 x = 14 = = 20 30 B’ 21 A’ = 2 3 8 2 y 3 y = 12 = 10 z z = 15 D’ D 20 C 10 A 30 15 12 8 14 B C’ A’ B’ 21 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 From the homework pg. 250 #1-4 pg. 251 #26