1 / 17

Understanding Triangles: Proportions, Similarity, and Parallel Line Segments

This chapter focuses on applying proportions to determine similarity in triangles and parallel line segments. It includes definitions, postulates, and theorems related to similar polygons and triangle properties. Key concepts such as the Property of Proportions, characteristics of similar shapes, and midsegment theorems are covered. Students will learn how to solve problems involving ratios and determine triangle similarity, ensuring they have a strong foundation in geometry.

xenos
Download Presentation

Understanding Triangles: Proportions, Similarity, and Parallel Line Segments

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. Ch 9.Rev Learning Target: I will be able to use proportions to determine similarity and parallel line segments of a triangle. Standard: various Ch 9.1 thru 9.5Review

  2. Ch 9.1 Concept

  3. a b a b c d c d = = Ch 9.1 Theorem 9-1 Property of Proportions For any numbers a and c and any nonzero numbers b and d, if , then ad = bc. Likewise, if ad = bc, then Concept

  4. Ch 9.1 Answers: 10) x = -15 9) x = 49 12) x = 4.5 11) x = ± 10

  5. Ch 9.2 Definition of Similar Polygons Concept

  6. Ch 9.2 Theorem 9-10 Concept

  7. 4 10 15 9 6 16 10 6 ≠ = Ch 9.2 15) not similar 16) PQRS~WXYZ Concept

  8. Ch 9.2 Answers: 13) 5x + 8x + 10x = 276; x = 12; 10(12) = 120 14) 3x + 2x = 12; x = 2 ⅖; 3(2 ⅖) = 7⅕, 2(2 ⅖) = 4 ⅘

  9. 3 50 15 + 10 + 13 x = Ch 9.2 x = 633 ⅓ Concept

  10. Ch 9.3 Postulate 9-1 Concept

  11. Ch 9.3 9-2 9-3 Concept

  12. Ch 9.3 not similar (shapes are not the same) IJK ~ HFG SSS Similarity not similar (angles are not congruent) TUV ~ TSR AA Similarity

  13. Ch 9.4 Theorem 9-5 Concept

  14. Ch 9.5 Theorem 9-6 Concept

  15. 240 200 8 18 4 x 5 12 10 x 300 x = = = Ch 9.4 x = 22.5 x = 9.6 x = 250 Concept

  16. Ch 9.5 Theorem 9-7 Concept

  17. Ch 9.5 (Justify your answer) IJ = 10.5 • Since FI = IG, then I is the midpoint. • Since FJ = JH, then J is the midpoint. • By definition, IJ is the midsegment. • By the Triangle Midsegment Theorem, IJ = ½ GH Concept

More Related