Proving Triangles Congruent

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem 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 theorem 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem 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 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

Which triangle congruence theorem is NOT a valid shortcut?

Back

SSA (Side-Side-Angle) is NOT a valid shortcut to prove triangles congruent.

Front

If two triangles have two angles equal, what can be said about their sides?

Back

The sides opposite those angles are proportional, but the triangles are not necessarily congruent unless the third side is also equal.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle between the two sides being compared, which is crucial for establishing congruence.

Front

Can AAA prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot prove triangle congruence because it only shows that triangles are similar, not necessarily congruent.

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.