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**Proportions and Similar Triangles**

8.6

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**Theorem 8.4 Triangle Proportionality Theorem**

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

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**Converse of the Triangle Proportionality Theorem**

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

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Example 1 4 8 12 In the diagram ll , BD=8,DC=4, and AE=12. What is the length of ?

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Example 2 Given the diagram, determine whether ll . 21 56 16 48

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Find x. 36x = 840 x = 23⅓

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Find x. 2(x + 6) = 5x 2x + 12 = 5x -2x x 12 = 3x 4 = x

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**Find x. 2.5(8 – x) = 3.5x 20 – 2.5x = 3.5x +2.5x +2.5x 20 = 6x 6 6**

3⅓ = x

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Find x. 7 x 3x = 31.5 3 4.5 x = 10.5

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**Find x. 6(x + 5) = 10x 6x + 30 = 10x -6x -6x 30 = 4x 4 4 7.5 = x x 6**

7.5 = x

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Find x. 12.8x = 115.2 x = 9

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Find x. 24x = 240 x = 10 in.

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Find x. 12x = 72 x = 6 ft.

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Theorem 8.6 If three parallel lines intersect two transversals, then they divide the transversals proportionally.

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Example

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Theorem 8.7 If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides.

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Example 14-x x

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Homework (day 36-Honors) p. 465 (11, 17, 19, 21, 23, 28, 31, 41) p. 474 (4, 8, 12, 18, 22, 30, 32, 40, 43, 46) Quiz next block (7.3, 7.4, 7.5)…TEST in.

Homework (day 36-Honors) p. 465 (11, 17, 19, 21, 23, 28, 31, 41) p. 474 (4, 8, 12, 18, 22, 30, 32, 40, 43, 46) Quiz next block (7.3, 7.4, 7.5)…TEST in.

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