Triangle Congruence Proofs

Front

What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the main criteria for triangle congruence?

Back

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

Front

Define SSS (Side-Side-Side) Congruence Criterion.

Back

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

Front

Define SAS (Side-Angle-Side) Congruence Criterion.

Back

SAS 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 ASA (Angle-Side-Angle) Congruence Criterion.

Back

ASA 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 AAS (Angle-Angle-Side) Congruence Criterion.

Back

AAS 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 (Hypotenuse-Leg) Congruence Criterion?

Back

HL states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent.

Front

What is the SSA (Side-Side-Angle) condition?

Back

SSA is not a valid criterion for triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you prove two triangles are congruent using the SSS criterion?

Back

To prove two triangles are congruent using SSS, measure all three sides of both triangles and show that they are equal.

Front

How can you prove two triangles are congruent using the SAS criterion?

Back

To prove two triangles are congruent using SAS, measure two sides and the included angle of both triangles and show they are equal.