9 2 Similar Polygons 9 2 Similar Polygons

9 -2 Similar Polygons

9 -2 Similar Polygons closed figure in a plane formed by segments called sides. A polygon is a ______ It is a general term used to describe a geometric figure with at least three sides.

9 -2 Similar Polygons Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding proportional sides are ______. D C G H Definition of Similar Polygons A B E F and Polygon ABCD ~ polygon EFGH

9 -2 Similar Polygons A) Determine if the polygons are similar. Justify your answer. 6 4 4 5 7 4 6 congruent 1) Are corresponding angles are _____. proportional 2) Are corresponding sides ______. = 28 = 30 The polygons are NOT similar!

9 -2 Similar Polygons B) Find the values of x and y if ΔRST ~ ΔJKL R 4 7 = 5 4 Write the proportion that can be solved for y. T 6 J S 6 y + 2 4(y + 2) = 42 4 y + 8 = 42 4 y = 34 7 x Write the proportion that can be solved for x. L 4 7 = 5 x 4 x = 35 y + 2 K

9 -2 Similar Polygons 1) Determine if the polygons are similar. Justify your answer. 3 10 6 5 4 8 congruent 1) Are corresponding angles are _____. proportional 2) Are corresponding sides ______. = = The polygons are similar!

9 -2 Similar Polygons 2) Find the values of x and y if ΔABC ~ ΔDEF A 3 2 = 5 3 Write the proportion that can be solved for y. B 4 D C 5 y - 1 3(y - 1) = 10 3 y - 3 = 10 3 y = 13 y - 1 2 Write the proportion that can be solved for x. E 3 2 = 3 x = 8 4 x x F

9 -2 Similar Polygons Scale drawings are often used to represent something that is too large or too small to be drawn at actual size. Contractors use scale drawings to represent the floorplan of a house. C) Use proportions to find the actual dimensions of the kitchen. . 75 in. length width 1 in 16 ft = 1. 25 in. 1 in w ft. 16 ft = . 75 in. L ft. (16)(1. 25) = w (16)(. 75) = L 20 = w 12 = L width is 20 ft. length is 12 ft. 1. 25 in. . 5 in. Dining Room Kitchen Utility Room Living Room Garage Scale: 1 in. = 16 ft.

9 -2 Similar Polygons Scale drawings are often used to represent something that is too large or too small to be drawn at actual size. Contractors use scale drawings to represent the floorplan of a house. 3) Use proportions to find the actual dimensions of the Utility Room. . 75 in. length width 1 in 16 ft = . 5 in. 1 in w ft. 16 ft (16)(. 5) = w 8 = w width is 8 ft. = . 75 in. L ft. 1. 25 in. . 5 in. Dining Room Kitchen Utility Room Living Room (16)(. 75) = L 12 = L length is 12 ft. Garage Scale: 1 in. = 16 ft.

End of section 9 -2 Assignment: Page 359 Problems 4 -22

9 -3 Similar Triangles