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10-4 Proportions and Similar Triangles

10-4 Thm: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the side proportionally.

Corollary to 10-4: 3 or more parallel lines intersect 2 transversals, then the segments are proportional.

Thm 10-5(Triangle Angle Bisector): If a ray bisects an angle of a triangle, then it divides the opposite side into 2 segments that are proportional to the other 2 sides of the triangle.

Example:

10-5 and 10-6 Proportions in Similar Figures

Similarity Ratio: The same as the perimeter ratio.

(S.R)squared=the area raito

The square root of the Area Ratio equals the Similarity Ratio.

YOU MUST REDUCE ALL RATIOS BEFORE YOU CONVERT!!!

Problem 10-4

Draw a small and a large triangle. Make the area of the smaller one 12 cm squared, and the area of the larger one 48 cm squared.

Therefore the Area Ratio is 12/48

When you reduce once, the area is 2/8. The second time it is 1/4, which is your answer.

Therefore, the perimeter is 1/2.