1 / 10

Applying Properties of Similar Triangles

Applying Properties of Similar Triangles. Students will be able to use properties of similar triangles to solve problems. 1. Triangle Proportionality Theorem. If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally . If

kenyon
Download Presentation

Applying Properties of Similar Triangles

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. Applying Properties of Similar Triangles Students will be able to use properties of similar triangles to solve problems

  2. 1. Triangle Proportionality Theorem • If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally. If then = Q S T R P Unit F

  3. Example 1: Using Triangle Proportionality Theorem J 18 Find the length of JN Use the Triangle Proportionality Theorem: K 12 L N 8 M 12 · JN = 8 · 18 JN = JN = 12 Unit F

  4. 2. Converse of the Triangle Proportionality Theorem • If a line divides two sides of a triangle proportionally, then it is parallel to the third line. If = then Q S T R P Unit F

  5. Example 2: Using the Converse of Triangle Proportionality AC = 36 cm, and BC = 27 cm. Verify that . Since , by the Converse of the Triangle Proportionality Theorem. Unit F

  6. 3. Two-Transversal Proportionality • If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. A B • If are parallel lines, then C D E F Unit F

  7. Example 3: Using the Two-Transversal • An artist used perspective to draw guidelines to sketch a row of parallel trees. What length would LN be? 8 in. 4 in. A BD = BC + CD = 4 + 5 = 9 in. 8 · LN = 90 LN = 11 in. 5 in. B C D N M L K 10 in. Unit F

  8. 4. Triangle Angle Bisector Theorem • An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides. If bisects ∠BAC, then Unit F

  9. Example 4: Using Triangle Angle Bisector Theorem • Find AC and DC. (8) = 4.5(y– 2) 4y = 4.5y - 9 → -.5y = -9 → y = 18 AC = y – 2 = 16 and Unit F

  10. Lesson Quiz Find the length of each segment. 1. 2. SR = 25, ST = 15 Unit F

More Related