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Proportional Parts

Proportional Parts. Lesson 5-4. F. C. A. B. D. E. Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. . Similar Polygons. C. B. 1. 2. D. A. 4. 3. E. Triangle Proportionality Theorem.

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Proportional Parts

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  1. Proportional Parts Lesson 5-4 Lesson 5-4: Proportional Parts

  2. F C A B D E Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. Similar Polygons Lesson 5-4: Proportional Parts

  3. C B 1 2 D A 4 3 E Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional length. Converse: If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side. Lesson 5-4: Proportional Parts

  4. B D E 6 9 C A x 4 B 4x + 3 2x + 3 D E 9 5 A C Examples……… Example 1: If BE = 6, EA = 4, and BD = 9, find DC. 6x = 36 x = 6 Example 2: Solve for x. Lesson 5-4: Proportional Parts

  5. Theorem A segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is one-half the length of the third side. R M L T S Lesson 5-4: Proportional Parts

  6. If two triangles are similar: (1) then the perimeters are proportional to the measures of the corresponding sides. Lesson 5-4: Proportional Parts

  7. E B F D C A 25 15 4 20 Example: Given: ΔABC ~ ΔDEF, AB = 15, AC = 20, BC = 25, and DF = 4. Find the perimeter of ΔDEF. The perimeter of ΔABC is 15 + 20 + 25 = 60. Side DF corresponds to side AC, so we can set up a proportion as: Lesson 5-4: Proportional Parts

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