Triangle Congruence Theorems

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 ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem stating that if two angles and the side between them in one triangle are equal to two angles and the side between them in 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 does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that if two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a 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

What is the SSA condition in triangle congruence?

Back

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

Front

What is the AAA condition in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which indicates that if three angles of one triangle are equal to three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal in length.

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, show that two angles and the side between them in one triangle are equal to the corresponding two angles and side in another triangle.

Front

How can you prove triangles are congruent using AAS?

Back

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