Congruent Triangles 1

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What does the SAS postulate state?

Back

The SAS (Side-Angle-Side) postulate 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 a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, typically written in the form of triangle names, such as ΔABC ≅ ΔDEF.

Front

How can you determine if two triangles are congruent?

Back

Two triangles can be determined to be congruent by using congruence postulates such as SSS, SAS, ASA, AAS, or HL.

Front

What does the SSS postulate state?

Back

The SSS (Side-Side-Side) postulate 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 ASA postulate?

Back

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS postulate state?

Back

The AAS (Angle-Angle-Side) postulate 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 is the HL theorem?

Back

The HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What is the importance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows for the application of congruence postulates and theorems to prove triangle congruence.

Front

How do you write a congruence statement for triangles?

Back

To write a congruence statement for triangles, list the vertices of the triangles in corresponding order, such as ΔABC ≅ ΔDEF, where A corresponds to D, B to E, and C to F.