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 if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Front

Why is AAA not a valid postulate for triangle congruence?

Back

AAA (Angle-Angle-Angle) is not a valid postulate for triangle congruence because it only proves that the triangles are similar, not necessarily 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

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, you must show that all three sides of one triangle are equal to the three sides of another triangle.

Front

How can you prove triangles are congruent using SAS?

Back

To prove triangles are congruent using SAS, you must show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, you must show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.