9.2 Similar Polygons

Vocabulary What You'll Learn Similar Polygons You will learn to identify similar polygons. Vocabulary 1) polygons 2) sides 3) similar polygons 4) scale drawing

Polygons that are the same shape but not necessarily the same size are Similar Polygons A polygon is a ______ figure in a plane formed by segments called sides. closed It is a general term used to describe a geometric figure with at least three sides. Polygons that are the same shape but not necessarily the same size are called ______________. similar polygons The symbol ~ is used to show that two figures are similar. ΔABC is similar to ΔDEF A B C D F E ΔABC ~ ΔDEF

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

Determine if the polygons are similar. Justify your answer. Similar Polygons Determine if the polygons are similar. Justify your answer. 7 6 6 4 5 4 5 7 1) Are corresponding angles are _________. congruent 2) Are corresponding sides ___________. proportional = 0.66 = 0.71 The polygons are NOT similar!

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

Contractors use scale drawings to represent the floorplan of a house. 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. Dining Room Kitchen Living Garage Utility 1.25 in. .75 in. 1 in. .5 in. Scale: 1 in. = 16 ft. Use proportions to find the actual dimensions of the kitchen. width length 1 in 1.25 in. 1 in .75 in. = = 16 ft w ft. 16 ft L ft. (16)(1.25) = w (16)(.75) = L 20 = w 12 = L width is 20 ft. length is 12 ft.

Perimeters and Similarity What You'll Learn You will learn to identify and use proportional relationships of similar triangles. Vocabulary 1) Scale Factor

Perimeters and Similarity These right triangles are similar! Therefore, the measures of their corresponding sides are ___________. proportional Use the ____________ theorem to calculate the length of the hypotenuse. Pythagorean 10 6 15 9 8 12 6 8 10 2 We know that = = = 9 12 15 3 Is there a relationship between the measures of the perimeters of the two triangles? perimeter of small Δ perimeter of large Δ = 9 + 12 + 15 6 + 8 + 10 = 36 24 = 3 2

Perimeters and Similarity Theorem 9-10 If two triangles are similar, then the measures of the corresponding perimeters are proportional to the measures of the corresponding sides. A C B F E D If ΔABC ~ ΔDEF, then perimeter of ΔABC perimeter of ΔDEF = DE AB = EF BC = FD CA

Perimeters and Similarity The perimeter of ΔRST is 9 units, and ΔRST ~ ΔMNP. Find the value of each variable. M N 4.5 P R S T 3 6 z Y x perimeter of ΔMNP perimeter of ΔRST RS MN = RS MN = ST NP RS MN = TR PM Theorem 9-10 2 3 = y 6 2 3 = z 4.5 13.5 9 x 3 = The perimeter of ΔMNP is 3 + 6 + 4.5 3y = 12 3z = 9 27 = 13.5x Cross Products x = 2 y = 4 z = 3

Perimeters and Similarity The ratio found by comparing the measures of corresponding sides of similar triangles is called the constant of proportionality or the ___________. scale factor D E F 14 10 6 A B C 7 5 3 DE AB = EF BC FD CA If ΔABC ~ ΔDEF, then or 6 3 = 14 7 10 5 2 1 The scale factor of ΔABC to ΔDEF is 2 1 Each ratio is equivalent to 1 2 The scale factor of ΔDEF to ΔABC is

End of section 9.2