Geometry: Congruent and Similar Figures

Front

What are congruent figures?

Back

Congruent figures are figures that have the same shape and size. They can be transformed into each other through rotations, translations, and reflections.

Front

What are similar figures?

Back

Similar figures are figures that have the same shape but not necessarily the same size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

How do you determine if two figures are similar?

Back

To determine if two figures are similar, check if their corresponding angles are equal and if the ratios of their corresponding sides are equal.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of two corresponding sides of similar figures.

Front

If a figure is reduced from (10, 15) to (5, 7.5), what is the scale factor?

Back

The scale factor is 1/2.

Front

What transformations can be used to show that two figures are congruent?

Back

Two figures can be shown to be congruent through rotations, translations, and reflections.

Front

What is the difference between congruence and similarity?

Back

Congruence means that figures are identical in shape and size, while similarity means that figures have the same shape but may differ in size.

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

Yes, if the corresponding angles are also equal, the triangles are similar.

Front

What does it mean for two figures to be not similar?

Back

Two figures are not similar if their corresponding angles are not equal or if the ratios of their corresponding sides are not equal.

Front

How can you prove that two triangles are similar using angle-angle (AA) similarity?

Back

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