Extension 3.6 Proportions and Similar Figures A.What do you know about similar triangles and congruent triangles? B.Definitions 1.Similar triangles – have the same shape, but not necessarily the same size Symbol: ~ similar characteristics: angles are congruent sides are in proportion 2. Congruent triangles – have the same shape and size Symbol: congruent characteristics: sides and angles are congruent C. Name the corresponding sides and angles. Then, solve for x if. B A C 15cm 21cm 18cm F D E 10cm x cm

Continued Examples: Given ABCD ~ FGHJ, find AD C B D A G H F J 40 m x 35 m 14 m Applying Similarity – Indirect Measurement 1.) A tree cast a shadow 7.5 ft long. A girl 5 ft tall casts a shadow 3 ft long. The triangle shown for the tree and its shadow is similar to the triangle shown for the woman and her shadow. How tall is the tree?

Review of Scale Drawing 1.) Scale Drawing – an enlarged or reduced drawing that is similar to an actual object or place. 2.) Scale – ratio of a distance in the drawing to the corresponding actual distance. Examples: 1.) The scale of the map of Pennsylvania says that 1 inch: 10miles. Approximately how far is it from York to Philadelphia if the map distance is 12.5 in. ? 2.) A blueprint for a house states that 2.5 inches equals 12 feet. If the length of a wall is 16feet, how long is the wall in the blueprint? 3.) A collector’s model racecar is scaled so that 1 inch on the model equals 6.25 feet on the actual car. If the model is 2/3 inch high, how high is the actual car?