Triangle SImilarities, Proportions, and Dilations

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the AA Similarity Theorem?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SAS Similarity Theorem?

Back

If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the SSS Similarity Theorem?

Back

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is a dilation in geometry?

Back

A transformation that alters the size of a figure but not its shape, defined by a scale factor.

Front

How do you perform a dilation of a point?

Back

Multiply the coordinates of the point by the scale factor.

Front

What is the scale factor in a dilation?

Back

The ratio of the length of a side of the image to the length of the corresponding side of the original figure.

Front

If triangle ABC is dilated by a scale factor of 2, what happens to its area?

Back

The area of triangle ABC will increase by a factor of 4 (since area scales by the square of the scale factor).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of the corresponding sides of similar triangles are proportional.