Triangle Congruence Postulates

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 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 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 does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate 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 HL stand for 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

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid postulate for proving triangle congruence because it can lead to ambiguous cases.

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, and it is crucial for establishing congruence.

Front

Can two triangles be congruent if only two sides are known?

Back

Not necessarily; without knowing the included angle, two triangles may not be congruent (SSA case).

Front

What is the difference between AAS and ASA?

Back

AAS requires two angles and a non-included side, while ASA requires two angles and the included side.

Front

How can you prove triangles are congruent using SSS?

Back

By showing that all three corresponding sides of two triangles are equal in length.