Triangle Postulates

Front

What does the HL theorem stand for in triangle congruence?

Back

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

Front

What does the SAS postulate state?

Back

SAS stands for Side-Angle-Side postulate, which states 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 the ASA postulate state?

Back

ASA stands for Angle-Side-Angle postulate, which states that 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 the AAS postulate state?

Back

AAS stands for Angle-Angle-Side postulate, which states 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 is the SSS postulate?

Back

SSS stands for Side-Side-Side postulate, which states that if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

Can two triangles be congruent if only their angles are known?

Back

No, if only the angles are known, the triangles may be similar but not necessarily congruent. This is known as the AAA condition.

Front

What is the difference between congruent 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

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 for establishing congruence in the SAS postulate.

Front

What is the significance of the included side in the ASA postulate?

Back

The included side is the side between the two angles being compared; it is essential for establishing congruence in the ASA postulate.

Front

What is the significance of the non-included side in the AAS postulate?

Back

The non-included side is the side that is not between the two angles being compared; it is essential for establishing congruence in the AAS postulate.