Triangle Congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

SAS stands for Side-Angle-Side, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle 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 postulate that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What is the HL postulate?

Back

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

Front

What does SSA stand for, and why is it not a valid postulate for triangle congruence?

Back

SSA stands for Side-Side-Angle. It is not a valid postulate for triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

How can you prove triangles are congruent using the SSS postulate?

Back

SSS stands for Side-Side-Side. If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are the same size and shape, while similarity means that triangles have the same shape but may be different sizes.

Front

Provide an example of using the AAS postulate to prove triangle congruence.

Back

If triangle ABC has angles A and B congruent to angles D and E in triangle DEF, and side AC is congruent to side DF, then triangle ABC is congruent to triangle DEF by AAS.

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle is the angle formed between the two sides being compared. It is crucial because it ensures that the triangles are congruent based on the specific arrangement of the sides.