Same Shape, Different Size

Part of the Triangles section of Coddy's Geometry journey. Lesson 51 of 71.

Two triangles are similar when one is an enlargement of the other. They have the same shape at a different size. Their matching angles are equal, pair by pair. Every side of the larger triangle is the same multiple of the matching side of the smaller triangle. That multiple is the scale factor.

$Two similar triangles, the second with every side twice the first, matching angles marked with matching arcs$

The second triangle is the first one at twice the size

In the figure, the scale factor is 2. Every side of the second triangle is twice the matching side of the first, and the matching angles are equal. To show that two triangles are similar, you only need two pairs of equal matching angles. The angles of a triangle add to 180°, so the third pair of angles must then be equal as well.