11.7 Ratios of Areas Objective: After studying this section you will be able to find ratios of areas by calculating and comparing the areas and applying.

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Presentation transcript:

11.7 Ratios of Areas Objective: After studying this section you will be able to find ratios of areas by calculating and comparing the areas and applying properties of similar figures.

One way to determine the ratio of the areas of two figures is to calculate the quotient of the two areas. Computing Areas Example Find the ratio of the area of the parallelogram to the area of the triangle

Example In the diagram, AB = 5 and BC = 2. Find the ratio of the area of triangle ABD to triangle CBD. D C B A

Similar Figures If two triangles are similar, the ratio of any pair of their corresponding altitudes, medians, or angle bisectors equals the ratio of their corresponding sides. WY X 4 P Q R 6

TheoremIf two figures are similar, then the ratio of their areas equals the square of the ratio of corresponding segments. (Similar Figures Theorem) Where A 1 and A 2 are areas and s 1 and s 2 are measures of corresponding segments.

Given the similar pentagons shown, find the ratio of their areas 12 9

Example 1 Example 2 If, find the ratio of the areas of the two triangles. FE D B A C 12 8 If the ratios of the areas of two similar parallelograms is 49:121, find the ratio of their bases.

Example 3 AM is the median of triangle ABC. Find the ratio Theorem A median of a triangle divides the triangle into two triangles with equal areas. A B M C P Q R S

Summary State in your own words how to find the area of a figure using the corresponding segments. Homework: worksheet