1.C: Proportions and Similar Polygons

Overview

The purpose of this lesson is to use properties of similar polygons and proportions to find unknown measures.

This lesson will address the following CCRS Standard(s) for Geometry:

7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale
8.G.5: Use informal arguments to establish facts about the angle sum and exterior angles of triangles, above the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so

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In this lesson we have learned:

Given the proportion $\frac{a}{b} = \frac{c}{d}$ , we can solve by multiplying diagonals to get ad = bc.
If to polygons are similar, then corresponding sides are proportional
If two angles of one triangle are congruent to two angles of another triangle, then the triangle's sides are proportional.