Triangle Congruence

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 SSS stand for in triangle congruence?

Back

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

Back

HL stands for Hypotenuse-Leg, a theorem that applies 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 congruent, meaning they have the same size and shape, which is essential in solving geometric problems.

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 congruent triangles and similar triangles?

Back

Congruent triangles have the same size and shape, while similar triangles have the same shape but may differ in size.

Front

Provide an example of using the SAS theorem.

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 triangles ABC and DEF are congruent by SAS.

Front

Provide an example of using the SSS theorem.

Back

If triangle GHI has sides GH = 4 cm, HI = 5 cm, and GI = 6 cm, and triangle JKL has sides JK = 4 cm, KL = 5 cm, and JL = 6 cm, then triangles GHI and JKL are congruent by SSS.