1 / 13

Geometry

In this lesson, we explore the theorems that prove triangle similarity, focusing on the SAS (Side-Angle-Side) and SSS (Side-Side-Side) similarity theorems. We begin by reviewing the definition of similar polygons, where all angles are congruent and all sides are proportional. The AA Postulate (Angle-Angle) is also examined as a method for proving similarity. We work through examples and problems to solidify understanding of how to confirm triangle similarity using these important theorems.

stephanie-hull
Télécharger la présentation

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 7.5 Theorems for Similar Triangles

  2. Two Triangles can be proved similar by using: • Definition of similar polygons • All angles congruent • All sides proportional • AA Postulate (2 angles = 2 angles) Today we learn 2 additional methods: • SAS Similarity Theorem • SSS Similarity Theorem

  3. SAS Similarity Theorem If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar. D ∆ABC ~ ∆DEF A 6 8 4 m<A = m<D 3 3 4 small = B C big E 6 8 F

  4. SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar. ∆ABC ~ ∆DEF D 4 6 8 small = = A big 6 9 12 6 9 6 4 B C E 8 12 F

  5. 4. 2. 3. A A 10 6 80 E D E D 3 80 5 C B B C L R F 3 5 16 24 20 10 M K N 6 6 H X S G 32 15 10 6 O R Q F 60 10.5 9 70 40 H G 70 P R X S S T 6 7 80 Problems: State the Method and Similarity Statement

  6. A B X C D 1. Given: Prove: AB || DC

  7. C Y A X B 2. Given: Prove:

  8. Homework pg. 264 CE #1-6 WE #1-13

  9. Similarity Chart All Polygons Triangles • Definition: • All angles congruent • All sides proportional • AAPostulate (2 <‘s = 2 <‘s) • SAS Similarity Theorem • SSS Similarity Theorem

  10. Properties of Similar ∆’s • Similarity has some of the same properties as equality and congruence. • These properties include: REFLEXIVE SYMMETRIC TRANSITIVE

  11. Name 2 similar ∆’s. Justify with a theorem. E 10 B 6 C 15 9 A D ∆ABC ~ ∆DEC by SAS Similarity ∆FHG ~ ∆XRS by SSS Similarity R F 20 16 24 10 H 15 G X 32 S

  12. Name 2 similar ∆’s. Justify with a theorem or postulate. A 80˚ D E 80˚ B C ∆CDE ~ ∆CAB by SAS Similarity ∆ADE ~ ∆ABC by AA Postulate C 6 10 D E 5 3 B A

  13. From the homework pg. 266 #3, 12

More Related