1 / 17

Geometry

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:

gerda
Download Presentation

Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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) 12 6 8 8 4 4 3 6

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

  6. 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

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

  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. F E F’ E’ A D A’ D’ B’ C’ B C ABCDEF ~ A’B’C’D’E’F’ 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: 20 18 30 8 z 12 v 6 15 y x 12

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

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

  12. EXAMPLE: Find m<B, m<Y, m<D and m<Z. D C Z 130 Y 130 60 60 X B A W 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

  13. Scale Factor • If two polygons are similar, then the ratio of the lengths of twocorresponding sides is called the scale factor. 6 2 4 12 1 3 = = 1 3 Scale factor is

  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 D’ 30 C’ D 20 z C 10 y 8 A B’ x B 21 A’

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

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

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

More Related