Section 8 3 Similar Polygons Similar polygons when

Section 8. 3: Similar Polygons

Similar polygons – when there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of the corresponding sides are proportional. The symbol ~ is used to indicate similarity.

In the diagram, ABCD is similar to EFGH. G F E ABCD ~ EFGH ~ H

Example 1: Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality. B C Q R P A D S

Angles: Sides: ~

Example 2: Determine whether the figures are similar. If they are, write the similarity statement. M P 10. 5 L 4 18 12 9 12 R N The triangles are not similar. Q

Example 3: Determine whether the figures are similar. If they are, write the similarity statement. WXYZ ~ PQRS

HOMEWORK (Day 1) pg. 476; 8 – 18

Scale factor – if two polygons are similar, then the ratio of the lengths of two corresponding sides is called a scale factor.

Theorem 8. 1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN ~ PQRS, then KL + LM + MN + NK PQ + QR + RS + SP KL = PQ = LM = MN = QR RS NK SP

Example 4: The rectangular patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters. Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft. , which is 3: 2 in simplified form. The perimeter of the patio is 2(24) + 2(48) = 144 feet and the perimeter of the pool is 2(16) + 2(32) = 96 feet 144 3 The ratio of the perimeters is , or 96 2 16 ft 32 ft 48 ft 24 ft

Example 5: Quadrilateral JKLM is similar to PQRS. Find the value of z.

Example 6: Parallelogram ABCD is similar to parallelogram GBEF. Find the value of y. B E G C 12 15 A F 24 y D

HOMEWORK (Day 2) pg. 477; 24 – 30, 39 – 42