Congruent Triangles

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does SSS stand for in triangle congruence?

Back

Side-Side-Side: A triangle congruence theorem stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side: A triangle congruence theorem stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle: A triangle congruence theorem stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side: A triangle congruence theorem stating 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

Hypotenuse-Leg: A triangle congruence theorem applicable to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

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

Back

No, at least two sides and the included angle or other congruence criteria must be known to prove congruence.

Front

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

Back

The included angle is the angle formed between the two sides being considered for congruence; it is crucial for establishing triangle congruence.

Front

What is the difference between SSA and other congruence criteria?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you prove triangles are not congruent?

Back

By showing that none of the congruence criteria (SSS, SAS, ASA, AAS, HL) can be satisfied with the given information.