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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

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Applying Properties of Similar Triangles

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  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

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