Similarity. Do Now What is the volume of the prism below: 3 in 2 in 7 in.

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Presentation transcript:

Similarity

Do Now What is the volume of the prism below: 3 in 2 in 7 in

Similar Polygons Two polygons are similar: All pairs of corresponding angles are congruent. The ratios of the lengths of all pairs of corresponding sides are equal. Ratio of Similtude = the ratio of the lengths of corresponding sides. The number represented by the ratio of similtude is called the constant of proportionally.

Example The following squares are similar. 4 in 7 in A B a. What is the ratio of similitude between squares A and B? b. What is the ratio of the areas of squares A and B?

Example The following right triangles are similar. 9 in A 6 in B 4 in 6 in a. What is the ratio of similitude between triangles A and B? b. What is the ratio of the area of triangles A and B?

Example The side of one cube measures 8 inches. The side of a smaller cube measures 6 inches. What is the ratio of the volumes of the two cubes (larger to smaller)? What is the ratio of similitude? 6 cm 8 cm

Example The rectangular prisms have dimensions as shown: 9 cm 6 cm 15 cm 10 cm a. Are the two figures similar? b. What is the ratio of their corresponding edges? c. What is the ratio of their surface areas? d. What is the ratio of their volumes? e. Justify your answers for c and d.

Example The sides of a triangle measures 4, 9, and 11. If the shortest side of a similar triangle measures 12, find the measures of the remaining sides of this triangle.

Example The sides of a quadrilateral measures 12, 18, 20, and 16. The longest side of a similar quadrilateral measures 5. Find the measures of the remaining sides of this quadrilateral.

Example In right triangle ABC, CD is the altitude to the hypotenuse, AB. The segments of the hypotenuse, AB are in the ratio of 1:4. The altitude is 6. Find the two segments.