Lesson 6: Similarity

Similarity

Student Summary

Let’s show that triangle $ABC$ is similar to triangle $DEF$ :

<p>Similar triangles. Ask for further assistance.</p><br>

Two figures are similar if one figure can be transformed into the other by a sequence of translations, rotations, reflections, and dilations. There are many correct sequences of transformations, but we only need to describe one to show that two figures are similar.

One way to get from triangle $ABC$ to triangle $DEF$ follows these steps:

Reflect triangle $ABC$ across line $f$
Rotate $90^\circ$ counterclockwise around $D$
Dilate with center $D$ and scale factor 2

Another way to show that triangle $ABC$ is similar to triangle $DEF$ would be to dilate triangle $DEF$ by a scale factor of $\frac12$ with center of dilation at $D$ , then translate $D$ to $A$ , then rotate it $90^\circ$ clockwise around $D$ , and finally reflect it across the vertical line containing $DF$ so it matches up with triangle $ABC$ .

Visual / Anchor Chart

Standards

Building On

8.G.2

Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

Addressing

8.G.4

Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.

8.G.2

Building Toward

8.G.4