Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem 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 SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are equal to all 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 theorem 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 HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem that states if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the significance of triangle congruence theorems?

Back

Triangle congruence theorems are used to prove that two triangles are identical in shape and size, which is essential in various geometric proofs and applications.

Front

Can SSA be used to prove triangle congruence?

Back

No, SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.

Front

Provide an example of using the SSS theorem.

Back

If triangle ABC has sides of lengths 5 cm, 7 cm, and 10 cm, and triangle DEF has sides of lengths 5 cm, 7 cm, and 10 cm, then by SSS, triangle ABC is congruent to triangle DEF.

Front

What is the criteria for using the SAS theorem?

Back

The SAS theorem can be used when two sides and the included angle of one triangle are known to be equal to two sides and the included angle of another triangle.