5.6 Proving Triangles Congruent

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence 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 criterion for triangle congruence 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence 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 AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence 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

HL stands for Hypotenuse-Leg, a criterion for triangle congruence 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 definition of congruent triangles?

Back

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

Front

When can triangles be considered not congruent?

Back

Triangles can be considered not congruent if none of the congruence criteria (SSS, SAS, ASA, AAS, HL) are satisfied.

Front

Provide an example of SSS congruence. What must be true?

Back

For SSS congruence, if Triangle ABC has sides AB = 5 cm, BC = 7 cm, CA = 8 cm, and Triangle DEF has sides DE = 5 cm, EF = 7 cm, FD = 8 cm, then Triangle ABC is congruent to Triangle DEF.

Front

Provide an example of ASA congruence. What must be true?

Back

For ASA congruence, if Angle A = 50°, Angle B = 60°, and side AB = 10 cm in Triangle ABC, and Angle D = 50°, Angle E = 60°, and side DE = 10 cm in Triangle DEF, then Triangle ABC is congruent to Triangle DEF.

Front

Provide an example of SAS congruence. What must be true?

Back

For SAS congruence, if Triangle GHI has sides GH = 6 cm, angle H = 45°, and HI = 8 cm, and Triangle JKL has sides JK = 6 cm, angle K = 45°, and KL = 8 cm, then Triangle GHI is congruent to Triangle JKL.