SSS, SAS, ASA, AAS Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a 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

SAS stands for Side-Angle-Side, a 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

ASA stands for Angle-Side-Angle, a 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

AAS stands for Angle-Angle-Side, a 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 is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

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

Back

If two triangles have two equal angles, the third angle must also be equal, and the triangles are congruent by the AAS theorem.

Front

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

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or two angles and a side must be equal.

Front

What is the relationship between SAS and SSS in triangle congruence?

Back

SAS can be derived from SSS; if all three sides are equal (SSS), then the angles must also be equal, thus satisfying SAS.

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; it is crucial for establishing congruence.

Front

If two triangles are not congruent, what can be said about their corresponding sides and angles?

Back

If two triangles are not congruent, at least one pair of corresponding sides or angles must be different.