Properties of Congruent Triangles

Front

What does CPCTC stand for in triangle congruence?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is used to prove that corresponding angles and sides of congruent triangles are equal.

Front

What are the three main triangle congruence theorems?

Back

The three main triangle congruence theorems are: 1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. AAS (Angle-Angle-Side)

Front

What is the SSS congruence theorem?

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 two 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 two 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 two triangles are congruent.

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

How can you prove that two triangles are congruent using CPCTC?

Back

To prove triangles are congruent using CPCTC, first establish that the triangles are congruent using a congruence theorem (like SSS, SAS, or AAS), then use CPCTC to show that corresponding parts (angles and sides) are equal.

Front

What is the significance of corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, which helps in proving triangle congruence and solving for unknown angles.

Front

If two triangles have two pairs of equal angles, what can be concluded about the triangles?

Back

If two triangles have two pairs of equal angles, the triangles are congruent by the AAS theorem.

Front

What is the relationship between the sides of congruent triangles?

Back

In congruent triangles, all corresponding sides are equal in length.