SSS, SAS, ASA, AAS, HL

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side', a postulate 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 postulate 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 postulate 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 postulate stating that if two angles and a non-included side of one triangle are equal to two angles and a non-included side of 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

When can we say two triangles are not congruent?

Back

Two triangles are not congruent if none of the congruence postulates (SSS, SAS, ASA, AAS, HL) can be applied to establish equality of sides and angles.

Front

Provide an example of SSS congruence.

Back

If triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm, and triangle DEF has sides of lengths 5 cm, 7 cm, and 9 cm, then triangle ABC is congruent to triangle DEF by SSS.

Front

Provide an example of SAS congruence.

Back

If triangle ABC has sides AB = 6 cm, AC = 8 cm, and angle A = 50 degrees, and triangle DEF has sides DE = 6 cm, DF = 8 cm, and angle D = 50 degrees, then triangle ABC is congruent to triangle DEF by SAS.

Front

Provide an example of ASA congruence.

Back

If triangle ABC has angles A = 30 degrees, B = 60 degrees, and side AB = 5 cm, and triangle DEF has angles D = 30 degrees, E = 60 degrees, and side DE = 5 cm, then triangle ABC is congruent to triangle DEF by ASA.

Front

Provide an example of AAS congruence.

Back

If triangle ABC has angles A = 40 degrees, B = 70 degrees, and side AC = 4 cm, and triangle DEF has angles D = 40 degrees, E = 70 degrees, and side DF = 4 cm, then triangle ABC is congruent to triangle DEF by AAS.