7-3 Similar Polygons

Similar Polygons When drawing pictures we do not always draw pictures to actual size. We draw them to scale. To draw something to scale means to draw it in the right shape but in a convenient size. Two figures drawn this way are called similar. Two polygons are similar if there vertices can paired so that : (1)ALL Corresponding angles are congruent (2) corresponding sides are in proportion. (Their lengths have the same ratio) When referring to similar polygons, their corresponding vertices must be listed in the same order.

Similar Polygons By definition of similar polygons we have:,,, R Q P S T 20 X Z W V 32 Y

Similar polygons Similarity has some of the same properties as equality and congruence. Similarity is reflexive, symmetric, and transitive. If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the Scale Factor of the similarity.

Similar Polygons Because we have similar polygons that means the ratios must be the same so R Q P S T 20 X Z W V 32 Y

Similar Polygons Since we know the length of similar pieces we can come up with the scale factor R Q P S T 20 X Z W V 32 Y

Similar Polygons Since we know the length of similar pieces we can come up with the scale factor The scale factor is R Q P S T 20 X Z W V 32 Y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters a) B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters a) B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters a) b) B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters a) b) B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters a) b) x = 14 y = 12 z = 15 B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = = 52 Perimeter of quad A’B’C’D’ = B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = = 52 Perimeter of quad A’B’C’D’ = = B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = = 52 Perimeter of quad A’B’C’D’ = = 78 d. Ratio of perimeters B A D C x 8 30 C’ D’ B’ A’ z 21 y

Similar Polygons Quad. ABCD ~ A’ B’ C’ D’. Find a.The scale factor b. values of x,y,z c.Perimeters of the two quadrilaterals d.The ratio of the perimeters c. Perimeter of quad ABCD = = 52 Perimeter of quad A’B’C’D’ = = 78 d. Ratio of perimeters B A D C x 8 30 C’ D’ B’ A’ z 21 y