Similar Triangles

Student Summary

Two polygons are similar when there is a sequence of translations, rotations, reflections, and dilations taking one polygon to the other. When the polygons are triangles, we only need to check that both triangles have two corresponding angles to show they are similar.

For example, triangle ABCABC and triangle DEFDEF both have a 30-degree angle and a 45-degree angle.

&lt;p&gt;Two triangles. First, A, B C. Angle A, 30 degrees, angle C, 45 degrees. Second, D, E, F. Angle D, 30 degrees, angle F, 45 degrees.&lt;/p&gt;<br>  

We can translate AA to DD and then rotate around point DD so that the two 30-degree angles are aligned, giving this picture:

Then a dilation with center DD and appropriate scale factor will move C′C' to FF. This dilation also moves B′B' to EE, showing that triangles ABCABC and DEFDEF are similar.

Visual / Anchor Chart

Standards

Building On
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.

7.RP.2.a

Recognize and represent proportional relationships between quantities.

Addressing
8.G.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

8.G.A

No additional information available.

Building Toward
8.G.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.