Algebra 1 Section 3.3

Definitions Similar figures have the same shape, but not necessarily the same size. Similar polygons are polygons in which corresponding angles are congruent & corresponding sides are proportional.

Similar Polygons Notation: ~ Example: ΔABC ~ ΔXYZ Corresponding vertices must be written in corresponding order.

Similar Polygons If ΔABC ~ ΔXYZ, then... A  X B  Y C  Z AB XY = BC YZ CA ZX

Example 1 CA ZY = AB XY 5m = 14.25 m = 14.25 5 5 2.5 = 5.7 m m = 2.85

Example 2 BC YZ = CA ZX 5n = 18.125 n = 18.125 5 7.25 n = 5 2.5

Example 2 The ratio of corresponding sides is 2. pABC = 5.7 + 7.25 + 5 = 17.95 pXYZ = 2.85 + 3.625 + 2.5 = 8.975 The ratio of corresponding sides is 2. The ratio of the perimeters is 2. = pABC pXYZ 17.95 8.975 = 2 = CA ZX 5 2.5 = 2

Similar Figures In any similar figures, the ratio of corresponding lengths, including perimeters, is equal to the ratio of their corresponding sides.

Example 3 It is convenient here to convert the lengths to feet. 53 = 5.25 ft 16 = 1.5 ft h 5.25 = 76 1.5

Similar Figures In any similar figures, the ratio of their areas is equal to the square of the ratio of any two corresponding sides.

Similar Figures In any similar figures, the ratio of their volumes is equal to the cube of the ratio of any two corresponding sides.

Example 4 Ratio of lengths: 2 to 3 a. Ratio of areas: 4 to 9 b. Ratio of volumes: 8 to 27 To find the area of the base of the larger prism: 36 AL = 4 9

Example 4 Ratio of lengths: 2 to 3 a. Ratio of areas: 4 to 9 b. Ratio of volumes: 8 to 27 To find the volume of the smaller prism: VS 1215 = 8 27

Example 4 AL = 81 units2 VS = 360 units3 Be sure to include any appropriate units with your answer!

Similar Figures Scale drawings are two- dimensional, such as maps, blueprints, and diagrams. Models are three-dimensional.

Definitions The scale of a drawing or model is the ratio of the dimensions of the drawing or model to the corresponding dimensions of the actual object.

Definitions In a scale drawing or model, all the dimensions are in the same scale or ratio to the actual dimensions of the object.

Example 5 17.5 in. × 11.25 in. × 11.5 in. 1:8 scale 17.5 x = 1 8 = 140 140 in.

Example 5 17.5 in. × 11.25 in. × 11.5 in. 1:8 scale 11.25 x = 1 8 = 90 90 in.

Example 5 17.5 in. × 11.25 in. × 11.5 in. 1:8 scale 11.5 x = 1 8 = 92 92 in. 140 in. × 90 in. × 92 in.

Homework: pp. 109-111