Triangle Congruence

Front

What is Triangle Congruence?

Back

Triangle Congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence include: 1) Side-Side-Side (SSS), 2) Side-Angle-Side (SAS), 3) Angle-Side-Angle (ASA), 4) Angle-Angle-Side (AAS), and 5) Hypotenuse-Leg (HL) for right triangles.

Front

Define Side-Side-Side (SSS) Congruence.

Back

SSS Congruence states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

Define Side-Angle-Side (SAS) Congruence.

Back

SAS Congruence 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

Define Angle-Side-Angle (ASA) Congruence.

Back

ASA Congruence 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 triangles are congruent.

Front

Define Angle-Angle-Side (AAS) Congruence.

Back

AAS Congruence 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 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 using SSS?

Back

To determine if two triangles are congruent using SSS, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What additional information is needed for SSS congruence?

Back

No additional information is needed for SSS congruence; knowing the lengths of all three sides is sufficient.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared. It is crucial because it ensures that the triangles are congruent based on the specific arrangement of the sides.