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

How can you prove triangles are not congruent?

Back

Triangles can be proven not congruent if any corresponding sides or angles do not match according to the congruence criteria (SSS, SAS, ASA, AAS, HL).

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important in geometry as it helps in establishing the equality of shapes, which is fundamental in proofs, constructions, and solving real-world problems.

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 ASA congruence.

Back

If triangle GHI has angles of 30° and 60° and the included side is 10 cm, and triangle JKL has angles of 30° and 60° with the same included side of 10 cm, then triangle GHI is congruent to triangle JKL by ASA.