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Proportions and Similar Triangles8.6
Theorem 8.4 Triangle Proportionality TheoremIf a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Converse of the Triangle Proportionality TheoremIf a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Example 1 4 8 12 In the diagram ll , BD=8,DC=4, and AE=12. What is the length of ?
Example 2 Given the diagram, determine whether ll . 21 56 16 48
Find x. 36x = 840 x = 23⅓
Find x. 2(x + 6) = 5x 2x + 12 = 5x -2x x 12 = 3x 4 = x
Find x. 2.5(8 – x) = 3.5x 20 – 2.5x = 3.5x +2.5x +2.5x 20 = 6x 6 6 3⅓ = x
Find x. 7 x 3x = 31.5 3 4.5 x = 10.5
Find x. 6(x + 5) = 10x 6x + 30 = 10x -6x -6x 30 = 4x 4 4 7.5 = x x 6 7.5 = x
Find x. 12.8x = 115.2 x = 9
Find x. 24x = 240 x = 10 in.
Find x. 12x = 72 x = 6 ft.
Theorem 8.6 If three parallel lines intersect two transversals, then they divide the transversals proportionally.
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.
Example 14-x x
You Can Do It!! Solve for x, y and z A B C D x y z 6 3.
Bellringer Solve for X.
Squares and Square Root WALK. Solve each problem REVIEW:
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Mrs. Rivas International Studies Charter School. Worksheet Practice 7-1 to 7-5Section 7-1 Algebra Solve each proportion.
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Section 6 – 6 Use Proportionality Theorem. Theorems Triangle Proportionality Theorem – If a line parallel to one side of a triangle intersects the other.
Math 310 Section 10.4 Similarity. Similar Triangles Def ΔABC is similar to ΔDEF, written ΔABC ~ ΔDEF, iff
LESSON 8.5 Proportions and Similar Triangles
Assignment P : 2-17, 21, 22, 25, 30, 31 Challenge Problems.
Quiz Topics Friday’s Quiz will cover: 1) Proportions(parallel lines and angle bisectors of triangles) 2) Pythagorean Theorem 3) Special Right Triangles.
8.6 Proportions & Similar Triangles
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Use Proportionality Themes
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Proportions in Triangles.
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