September 12th Triangle Congruence Theorems

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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, 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 included side of another triangle, 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, 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, the triangles are congruent.

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid theorem for proving triangle congruence because it can lead to ambiguous cases.

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 two triangles be congruent if only one side is known?

Back

No, knowing only one side is not sufficient to prove triangle congruence; at least two sides and the included angle or two angles and a side must be known.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in shape and size, 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.