Properties of Congruent Triangles

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 are corresponding angles?

Back

Corresponding angles are pairs of angles that are in the same position on two different parallel lines cut by a transversal.

Front

If ΔPRS ≅ ΔCFH, what can we conclude about their corresponding sides and angles?

Back

The corresponding sides and angles of ΔPRS and ΔCFH are equal.

Front

What does the SSS Congruence Theorem state?

Back

The SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the SAS Congruence Theorem?

Back

The SAS (Side-Angle-Side) Congruence Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the relationship between similar triangles and congruent triangles?

Back

All congruent triangles are similar, but not all similar triangles are congruent. Similar triangles have the same shape but may differ in size.

Front

How can you determine if two triangles are congruent using the properties of their angles?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are congruent by the AA (Angle-Angle) criterion.

Front

What is the definition of corresponding sides?

Back

Corresponding sides are sides that are in the same relative position in two different triangles.

Front

If angle C corresponds to angle Q, what can we say about their measures?

Back

The measures of angle C and angle Q are equal.