4.7 Congruent Postulates

Front

What does the ASA postulate state?

Back

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What is the SSS postulate?

Back

The SSS (Side-Side-Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Front

Define the SAS postulate.

Back

The SAS (Side-Angle-Side) postulate 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 two triangles are congruent.

Front

What is the AAS postulate?

Back

The AAS (Angle-Angle-Side) postulate states that 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 two triangles are congruent.

Front

What does the HL postulate refer to?

Back

The HL (Hypotenuse-Leg) postulate states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

What additional information is needed to prove triangles are congruent by HL?

Back

To prove triangles are congruent by HL, you need to know that the hypotenuses are congruent and one leg is congruent.

Front

If two triangles have two angles congruent, what can be said about the triangles?

Back

If two triangles have two angles congruent, the triangles are similar, but not necessarily congruent unless the sides are also proportional.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that two triangles are identical in shape and size, while similarity means that two triangles have the same shape but may differ in size.

Front

Can two triangles be congruent if only one side is known to be congruent?

Back

No, at least two sides and the included angle or specific postulates must be used to prove congruence.

Front

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

Back

The included angle in the SAS postulate is crucial because it ensures that the two sides are connected, which helps establish the congruence of the triangles.