4.7 Congruent Postulates

Front

What does the SSS postulate state?

Back

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

Front

What does the SAS postulate state?

Back

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

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 equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS postulate state?

Back

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

Front

What does the HL postulate state?

Back

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

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

If two triangles have two equal angles and one equal side, are they congruent?

Back

Yes, they are congruent by the AAS postulate.

Front

If two triangles have two equal sides and the included angle, are they congruent?

Back

Yes, they are congruent by the SAS postulate.

Front

Can two triangles be congruent if only one side is equal?

Back

No, at least two sides and the included angle or two angles and a side must be equal for the triangles to be congruent.

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.