# Lesson 11

Similarity

Let’s explore similar figures.

### Problem 1

Each diagram has a pair of figures, one larger than the other. For each pair, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.

### Problem 2

Here are two similar polygons.

Measure the side lengths and angles of each polygon. What do you notice?

### Problem 3

Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.

### Problem 4

Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.

1. Draw the translated image of $$ABCDE$$ so that vertex $$C$$ moves to $$C’$$. Tracing paper may be useful. 2. Draw the reflected image of Pentagon $$ABCDE$$ with line of reflection $$\ell$$. Tracing paper may be useful. 3. Draw the rotation of Pentagon $$ABCDE$$ around $$C$$ clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful. 