Similarity and Congruence

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

The SAS similarity criterion states that 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 Angle-Angle (AA) similarity criterion?

Back

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the definition of a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you determine if two ratios form a proportion?

Back

Two ratios form a proportion if the cross products are equal.

Front

If two triangles are similar, how do you find the length of a missing side?

Back

To find the length of a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides.

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 corresponding sides of similar triangles are in proportion.

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.