Triangle Congruence

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate that states 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

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states 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

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the AAA criterion in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which is not a valid criterion for triangle congruence because it only proves that triangles are similar, not congruent.

Front

What is the HL theorem in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem that states 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

How can you prove triangles are congruent using the AAS criterion?

Back

To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle in the SAS postulate is the angle formed between the two sides being compared, which is crucial for establishing congruence.

Front

Can two triangles be congruent if only one side is known?

Back

No, knowing only one side is not sufficient to prove triangle congruence; at least two sides and the included angle or two angles and a side must be known.

Front

What is the relationship between congruent triangles and their corresponding parts?

Back

If two triangles are congruent, then all their corresponding sides and angles are equal.