2 8 Proportions and Similar Figures Similar Figures

2 -8 Proportions and Similar Figures

Similar Figures: Have the same shape but not necessarily the same size The measures of corresponding angles are equal, and corresponding side lengths are proportional The order of the letters when you name the figures is so important because it tells you which parts of the figure are corresponding parts

In the figure below identify all the corresponding sides and angels

Problem 1: Finding the Length of a Side

Problem 2: Applying Similarity The sun’s rays strike the building and the girl at the same angle, forming two similar triangles shown. How tall is the building

Problem 2: Applying Similarity A man who is 6 feet tall is standing next to a flag pole. The shadow of the man is 3. 5 feet and the shadow of the flag pole is 17. 5 feet. What is the height of the flagpole?

Scale drawing: a drawing that is similar to an actual object or place (floor plans, blueprints, maps) Scale: the ratio of any length on the drawing to the actual length

Problem 3: Interpreting Scale Drawings What is the actual distance from Jacksonville to Orlando? 1 in: 110 mi

The distance from Jacksonville to Gainesville on the map is about 0. 6 in. What is the actual distance? 1 in: 110 mi

Scale Model: a three-dimensional model that is similar to a threedimensional object

Problem 4: Using Scale Models A giant model heart is shown below. The heart is the ideal size for a man who is 170 ft. tall. About what size would you expect the heart of the man who is 6 ft. tall to be?

A scale model of a building is 6 in tall. The scale of the model is 1 in: 50 ft. How tall is the actual building?