Objectives To identify similar polygons. To apply similar polygons.

Vocabulary Similar Similarity Ratio Golden Rectangle Golden Ratio

Similar Figures Similar figures are figures that have the same shape, but not necessarily the same size.

Similar Polygons Two polygons are similar if: Corresponding angles are congruent. Corresponding sides are proportional.

Similarity Ratio The ratio of the lengths of corresponding sides is the similarity ratio.

Understanding Similarity ABCD ~ EFGH

Determining Similarity Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio.

Using Similar Figures LMNO ~ QRST Find the value of x.

Golden Rectangle A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.

Golden Ratio In any golden rectangle, the length and the width are in the golden ratio, which is about 1.618…..:1

Golden Ratio in Art The Mona Lisa is one piece of art work that contains the golden ratio.

Example: Art An artist plans to paint a picture. He wants the canvas to be a golden rectangle with its longer horizontal sides 30 cm wide. How high should the canvas be?