Warmup on Proving Triangles 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 their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

Explain the SSS congruence criterion.

Back

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

Front

Explain the SAS congruence criterion.

Back

The SAS (Side-Angle-Side) criterion 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

Explain the ASA congruence criterion.

Back

The ASA (Angle-Side-Angle) criterion 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

Explain the AAS congruence criterion.

Back

The AAS (Angle-Angle-Side) criterion 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 HL congruence criterion?

Back

The HL (Hypotenuse-Leg) criterion 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 triangles are congruent.

Front

What does it mean if two triangles are not congruent?

Back

If two triangles are not congruent, it means that their corresponding sides and angles are not equal, indicating that they differ in size or shape.

Front

How can you determine if triangles are congruent using the SSS criterion?

Back

To determine if triangles are congruent using the SSS criterion, measure the lengths of all three sides of both triangles and compare them. If all three pairs of sides are equal, the triangles are congruent.

Front

How can you determine if triangles are congruent using the SAS criterion?

Back

To determine if triangles are congruent using the SAS criterion, measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, the triangles are congruent.