similar triangles

Two triangles are called “similar” if their corresponding angles have the same measure.      

a A b B c C Two triangles are called “similar” if their corresponding angles have the same measure.  Ratios of corresponding sides are equal. C A  a c     b B a A b B c C = =

application

Mary is 5 ft 6 inches tall. She casts a 2 foot shadow. The tree casts a 7 foot shadow. How tall is the tree?

Mary is 5 ft 6 inches tall. She casts a 2 foot shadow. The tree casts a 7 foot shadow. How tall is the tree? Mary’s height Tree’s height Mary’s shadow Tree’s shadow = x 5.5 2 7

Mary is 5 ft 6 inches tall. She casts a 2 foot shadow. The tree casts a 7 foot shadow. How tall is the tree? 5.5 x 2 7 = Mary’s height Tree’s height Mary’s shadow Tree’s shadow = x 5.5 2 7

5.5 x 2 7 = 7 ( 5.5 ) = 2 x 38.5 = 2 x x = 19.25 The height of the tree is 19.25 feet