Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Goals Identify similar polygons Find the ratio of similarity between similar figures. Solve problems involving similar figures. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons ABCD and RSTV are similar polygons: Corresponding angles are congruent. Corresponding sides are proportional. A B C D 15 12 9 R S T V 10 8 6 6 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Corresponding angles are congruent: A  R, B  S, C  T, D  V A B C D 15 12 9 R S T V 10 8 6 6 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Corresponding sides are proportional: A B C D 15 12 9 S 6 R 6 T 10 8 V May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Corr. s  Sides prop. ABCD ~ RSTV A B C D 15 12 9 R S T V 10 8 6 6 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Corresponding Angles are congruent. Corresponding Sides are proportional. Use the symbol “~” for similar. To show that two polygons are similar, you must prove both things: angles congruent, sides proportional. May 31, 2018 Geometry 8.3 Similar Polygons

Similarity Statements List the congruent angles. Write the ratios of the corresponding sides. J  Q, K  S, L  R 70 J K L Q R S May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Example Are these figures similar? Yes Why? Corr. angles congruent Corr. sides proportional. 3 E F 2 1.5 H G 4 N 6 M 4 3 O 8 P May 31, 2018 Geometry 8.3 Similar Polygons

Write the similarity statements. 3 E F 2 1.5 H G 4 N 6 M 4 3 O EFGH ~ NMPO 8 P Or: HEFG ~ ONMP, GFEH ~ PMNO, EHGF ~ NOPM, etc. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Scale Factor If two polygons are similar, the ratio of two corresponding sides is called the scale factor. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Scale Factor The scale factor of JKL to QSR is 10/5 or 2/1. The scale factor of QSR to JKL is 5/10 or 1/2. 70 J K L Q R S 10 5 May 31, 2018 Geometry 8.3 Similar Polygons

Perimeter and Similar Figures ABCD ~ FGHI Find the scale factor of ABCD to FGHI. Find the values of x, y, and z. Find the perimeter of ABCD and FGHI. Find the ratio of the perimeters. A B C D F G H I 10 4 14 5 z y x May 31, 2018 Geometry 8.3 Similar Polygons

Perimeter and Similar Figures 2. Find the scale factor from ABCD to FGHI. The only known corresponding sides are AB and FG. A B C D F G H I 10 4 14 5 z y x May 31, 2018 Geometry 8.3 Similar Polygons

Perimeter and Similar Figures 3. Find the values of x, y, and z. A B C D F G H I 10 4 14 5 z y x May 31, 2018 Geometry 8.3 Similar Polygons

Perimeter and Similar Figures 4. Find the perimeter of ABCD and FGHI. P = 42 P = 21 A B C D F G H I 10 4 14 5 2 7 May 31, 2018 Geometry 8.3 Similar Polygons

Perimeter and Similar Figures 5. Find the ratio of the perimeters. Ratio of perimeters 2:1 Ratio of Similarity 2:1 P = 42 P = 21 A B C D F G H I 10 4 14 5 2 7 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths and is equal to the similarity ratio. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Theorem 8.1 Example These figures are similar. Find the perimeter of the smaller one. 20 8 P = 100 P = ? May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problems to Solve May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 1 Solve for x and y if the triangles are similar. 20 x + 6 8 4 y – 2 6 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 1 Solution Scale Factor is 20/8 20 x + 6 8 4 y – 2 6 Solve for x Solve for y May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 2 Find x and y if the figures are similar. x + 10 85 100 32 60 24 y 95 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 2 Solution 60 x + 10 95 85 100 y 24 32 Similarity Ratio y = 360 - 100 - 85 - 95 y = 80 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 3 ABC ~ RST AB = 20 ST = 4 BC = RS Find BC and RS. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 3 Solution A B C R S T ABC ~ RST AB = 20 ST = 4 BC = RS Find BC and RS. 20 x 4 x May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 3 Solution A B C R S T 20 4 x ABC ~ RST May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 4 You want to print a picture in your camera. You have two sizes of paper for your printer: 4 × 6 and 5 × 7. Does it matter? Will the pictures printed from each size of paper be similar? 4 × 6 Sides not proportional, figures not similar. 5 × 7 May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Problem 5 MNOP has a perimeter of 24. Find the perimeter of QRST if MN = 8 and QR = 12. May 31, 2018 Geometry 8.3 Similar Polygons

Geometry 8.3 Similar Polygons Summary Two polygons are similar if they have the same shape, but a different size. If polygons are similar corresponding angles are congruent, and corresponding sides are proportional. The ratio of any two corresponding sides is the scale factor. The ratio of the perimeters is equal to the ratio of two corresponding sides. May 31, 2018 Geometry 8.3 Similar Polygons