Triangle Congruence Theorems

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that 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 AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem 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, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that if all three sides of one triangle are equal to all three sides 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 theorem stating that if two angles and the included side of one triangle are equal to two angles and the corresponding 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 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, 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 AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily congruent.

Front

Provide an example of SAS in triangle congruence.

Back

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60 degrees, and triangle DEF has sides DE = 5 cm, DF = 7 cm, and angle D = 60 degrees, then triangle ABC is congruent to triangle DEF by SAS.

Front

Provide an example of AAS in triangle congruence.

Back

If triangle GHI has angles G = 50 degrees, H = 60 degrees, and side GH = 8 cm, and triangle JKL has angles J = 50 degrees, K = 60 degrees, and side JK = 8 cm, then triangle GHI is congruent to triangle JKL by AAS.

Front

Provide an example of SSS in triangle congruence.

Back

If triangle MNO has sides MN = 6 cm, NO = 8 cm, and OM = 10 cm, and triangle PQR has sides PQ = 6 cm, QR = 8 cm, and RP = 10 cm, then triangle MNO is congruent to triangle PQR by SSS.