Similar Figures and Proportions
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1 Practice A Similar Figures and Proportions Identify the corresponding sides. 1. AB corresponds to. 2. BC corresponds to. 3. AC corresponds to. Identify the corresponding sides. Then use ratios to determine whether the triangles are similar Use the properties of similarity to determine whether the figures are similar
2 Practice B Similar Figures and Proportions Tell whether the triangles are similar Tell whether the figures are similar
3 CODE Practice C Similar Figures and Proportions Tell whether the figures are similar _ The figures in each pair are similar. Find the missing lengths or angle measures _
4 Review for Mastery Similar Figures and Proportions Figures that have the same shape but not the same size are similar figures. In similar figures, the ratio of the lengths of the corresponding sides are proportional, and the corresponding angles have equal measures. To determine if ABC is similar to XYZ, you can write a proportion for each pair of corresponding sides. longest sides middle sides shortest sides AB XY BC YZ The corresponding sides are always in the ratio 3. So the triangles are similar. 2 If a polygon has more than 3 sides, you must also show that the corresponding angles are equal. AC XZ Identify the corresponding sides. Use ratios to determine whether the figures are similar _ 3. TU EF 8 1 ; SU ; ST Are the ratios proportional? Are the triangles similar? 4. PQ PR ; ; QR Are the ratios proportional? Are the triangles similar?
5 _
6 Challenge The Same, Only Bigger You can sometimes create a similar figure by using copies of the original figure. Notice that the scale factor tells you how many times to repeat the original figure along each side or edge of the similar figure. Use the given scale factor and copies of the original figure to draw a figure similar to the original figure Draw a figure in the space below. Use a scale factor of 2 to create a similar figure.
7 Problem Solving Similar Figures and Proportions Use the information in the table to solve problems A small reproduction of one of the paintings in the list is similar in size. The reproduction measures 11 inches by 10 inches. Of which painting is this a reproduction? 2. A local artist painted a reproduction of Cézanne s painting. It measures 88 inches by 72 inches. Is the reproduction similar to the original? What is the ratio of corresponding sides? Painting Mona Lisa The Dance Class The Blue Vase Original Artist Size (in.) Leonardo da 30 by 21 Vinci Edgar Degas 33 by 30 Paul Cézanne 22 by A poster company made a poster of da Vinci's painting. The poster is 5 feet long and 3.5 feet wide. Is the poster similar to the original Mona Lisa? What is the ratio of corresponding sides? _ Choose the letter for the best answer. 4. Triangle ABC has sides of 15 cm, 20 cm, and 25 cm. Which triangle could be similar to triangle ABC? A A triangle with sides of 3 cm, 4 cm, and 5 cm B A triangle with sides of 5 cm, 6 cm, and 8 cm C A triangle with sides of 30 cm, 40 cm, and 55 cm D A triangle with sides of 5 cm, 10 cm, and 30 cm 6. A rectangle is 12 meters long and 21 meters wide. Which dimensions correspond to a nonsimilar rectangle? A 4 m; 7 m B 8 m; 14 m C 20 m; 35 m D 24 m; 35 m 5. A rectangular picture frame is 14 inches long and 4 inches wide. Which dimensions could a similar picture frame have? F Length 21 in.; width 8 in. G Length 35 in.; width 15 in. H Length 49 in.; width 14 in. J Length 7 in.; width 3 in. 7. A rectangle is 6 feet long and 15 feet wide. Which dimensions correspond to a similar rectangle? F 8 ft; 24 ft G 10 ft; 25 ft H 15 ft; 35 ft J 18 ft; 40 ft
8 Reading Strategies Understanding Vocabulary Similar means almost the same. If two objects are similar, they have some things in common. Similar figures are figures that are nearly the same. Similar figures have the same shape, but are different sizes. Similar figures have corresponding sides and corresponding angles. Corresponding means matching. Each side and angle in a similar figure has a corresponding side and angle. These two triangles are similar. Use the figures above to answer each question. 1. What angle corresponds to angle B? 2. What angle corresponds to angle A? 3. What side corresponds to side BC? Are the figures similar? Answer yes or no for each pair
9 Puzzles, Twisters & Teasers Concentrating on Figures Pretend this is a game of concentration. The object of the game is to match cards with similar figures. Each box represents a card with a figure on it. When you match 2 cards, cross them out. Rearrange the letters of the unmatched cards to solve the riddle. What kind of flowers are on your face?
10 LESSON 4-8 Practice A 1. XY 2. YZ 3. XZ 4. similar; AB DE BC EF AC DF ; not similar; JK MN KL NP ; similar; GH RS HJ ST GJ RT ; Possible answer: similar; XY UV YZ VW XZ UW ; not similar; AB QR BC RS ; similar; GH WX HJ XY JK YZ GK WZ ; Practice B 1. not similar; AB DE BC EF ; A 68, B 74, C 90, D 128 Review for Mastery 1. 16; 2; 2. FG; ; 4 3 ; DF; 12 6 ; 2 1 ; FH; ; 4 3 ; 2. similar; RS UV ST VW RT UW ; similar; XY JL YZ JK XZ KL ; not similar; FG QR EF PQ EG PR ; similar; AB EF AD EH ; not similar; corresponding angles are not equal Practice C 1. similar; XY RS YZ ST XZ RT ; not similar; BC DE AB EF AC DF ; not similar; WX NO ZY MP WZ MN XY OP ; not similar; angles are not equal 5. BC 6 in. 6. M 29, N 103, L FJ 4.9 cm DE; 10 4 ; 5 ; 2 GH; ; 4 3 ; no; no yes; yes 3. similar 4. not similar; angles not equal measure
11 Challenge Drawings will vary. Possible drawing given. 3. Problem Solving 1. The Dance Class 2. yes; 1:4 3. yes; 1:2 4. A 5. H 6. D 7. G Reading Strategies 1. angle E 2. angle D 3. side EF 4. yes 5. no Puzzles, Twisters & Teasers Similar figures: R and C; A and G; W and O; Y and E; F and N T U L I P S
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