Lesson 6

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.

Coordinate plane, x 0 to 4, y 0 to 6. Line through point A, the origin, C at 1 comma 2, E at 3 comma 6. Segments connect A, & C to point B at 1 comma 0. Segments connect E & C to point F at 3 comma 2.
Two triangles on a circular grid. Ask for further assistance.

Problem 2

Here are two similar polygons.

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

figure ABCD and figure EFGH on a grid.

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.

Triangles A, B C, and A prime B C prime. A prime lies on side A, B. C prime lies on side B C.
Triangles A, B C, and A, B prime C prime. B prime lies on side A, B. C prime lies on side A, C.