1 / 9

CHAPTER 8: Sections 8.1-8.3

CHAPTER 8: Sections 8.1-8.3. By: THE “A” SQUAD (Annie and Andrew). Vocabulary Terms. Dilation : A transformation that is not rigid and preserves the shape of an object despite size changes. Scale Factor : The number that both X and Y are multiplied by to get the Image.

zahir-irwin
Download Presentation

CHAPTER 8: Sections 8.1-8.3

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. CHAPTER 8: Sections 8.1-8.3 By: THE “A” SQUAD (Annie and Andrew)

  2. Vocabulary Terms • Dilation: A transformation that is not rigid and preserves the shape of an object despite size changes. • Scale Factor: The number that both X and Y are multiplied by to get the Image. • Similar Figures: Figures are similar when the image of the other is congruent by a dilation.

  3. Postulates and Theorems • Polygon Similarity Postulate: Two polygons are similar if and only if there is a way of setting up a correspondence between their sides and angles such that each pair of corresponding angles is congruent and each pair of corresponding sides is proportional. • Angle-Angle Postulate: If two angles are congruent to two angles of another triangle, then the triangles are similar. • Side-Side-Side Theorem: If three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar. • Side-Angle-Side Theorem: If two sides and their included angle are proportional/congruent respectively, then the triangles are similar.

  4. A Examples: D 14 Given: AB= 8; BC= 3; AC= 14; DE= 4; EF= 1.5; DF= 7 Prove: Triangle ABC ~ Triangle DEF 8 7 4 E F B C 3 1.5 AB/DE= 8/4= 2 BC/EF= 3/1.5= 2 AC/DF= 14/7= 2 Thus, the sides of the triangles are proportion and, by the SSS Similarity Theorem, Triangle ABC ~ Triangle DEF.

  5. More Examples: Given: <x = 25; <g = 25; xy = 2; xz = 3.6; fg= 3; gh = 5.4 Prove: Triangle XYZ ~ Triangle GFH g x 25 25 2 3.6 5.4 3 y z f h YX/FG = 2/3 XZ/GH = 3.6/5.4 = 2/3 Thus, the sides of the triangle are proportional, and the included angles of these sides are congruent. By the SAS Similarity Theorem, Triangle QRS ~ Triangle UTV.

  6. Daily Application

  7. Quiz: • Find the image of (3,3) for a dilation with scale factor 1/3. • Write a similarity statement for the two triangles. (1,1) E ABC ~ FED ACB ~ FDE BAC ~ EFD BCA ~ EDF CBA ~ DEF CAB ~ DFE B 54 65 D F 61 A C

  8. Quiz Continued 3. Find x and y for these similar rectangles. 18 6 x y 4 4 6 18 6/18 = 4/x 6x = 72 x =12 y = 12

  9. For more information… • http://www.mathwarehouse.com/geometry/similar/triangles/index.html

More Related