Similarity 7.2

Review 1.If ΔQRS ΔZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. (hint: cross multiply) 2. 3.

Vocabulary Similar (~) – exactly the same shape not necessarily the same size Similar Polygons – two polygons whose corresponding angles are congruent and corresponding sides are proportional. Similarity Ratio – ratio of the lengths of corresponding sides Ratio can be written: a : b a/b a to b

Match the similar figures. 1. a. b. c. 2. a. b.c.

Checking for Similarity In order to be similar, you must check for: – all corresponding angles congruent – all corresponding sides are proportional (meaning the ratios of each pair of matching sides is the same) – This ratio is the Similarity Ratio – You can then write a Similarity Statement: ∆ABC ~ ∆XYZ (order matters)

Describing similar polygons 1. Identify the pairs of congruent angles and corresponding sides. ZY X Q S R S R Q

2. Identify the pairs of congruent angles and corresponding sides. B C A 59° R S T

Determine if the polygons are similar. If so, write the similarity ratio and a similarity statement. 4. PQ R 10 36° 10 S T W 62° A C D B 6 9FG H E 6 4

Whiteboards Determine if the polygons are similar. If so, write the similarity ratio and a similarity statement. 6. P Q R 12 16° 12 S T W 82° J M L P NS

7. Find the length of the model to the nearest tenth of a centimeter. Race car Model 5 m 2 m 6 cm x Do on white boards!

Use similarity ratios to solve for the missing side J M L 8 10 P NS x A C D B 3 6 FG H E 3 x 3. P Q R 10 20° 10 S T W 80° 55 x 4

You try… 1.Identify the pairs of congruent angles and corresponding sides. 2.Determine if the parallelograms are similar. If so write the similarity ratio and similarity statement. If not explain why not. 3.Leonardo da Vinci’s famous portrait, the Mona Lisa, is 30 in long and 21 in wide. Janelle has a refrigerator magnet of the painting that is 3.5 cm wide. What is the length of the magnet? A BC X YZ F E G H T U V W 25

Assignment P 375 # 1-16