Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side', a postulate that states if three sides of one triangle are equal to 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 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 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 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 applies 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, then the triangles are congruent.

Front

If two triangles have sides of lengths 5, 12, and 13, are they congruent to a triangle with sides of lengths 5, 12, and 13?

Back

Yes, they are congruent by the SSS postulate.

Front

If triangle ABC has sides AB = 7, AC = 10, and angle A = 60°, what postulate can be used to prove triangle A'B'C' with AB' = 7, AC' = 10, and angle A' = 60° is congruent?

Back

The ASA postulate can be used to prove the triangles are congruent.

Front

What is the condition for two triangles to be congruent by the SAS postulate?

Back

Two triangles are congruent by the SAS postulate if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

If triangle DEF is congruent to triangle XYZ, and DE = 8, EF = 6, and angle E = 50°, what are the corresponding sides and angles in triangle XYZ?

Back

The corresponding sides are XY = 8, YZ = 6, and angle Z = 50°.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same shape and size, which means their corresponding sides and angles are equal.