Triangle Congruence

Front

What does the ASA postulate state?

Back

The Angle-Side-Angle (ASA) 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 Side-Side-Side (SSS) 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 Side-Angle-Side (SAS) 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 does the AAS postulate indicate?

Back

The Angle-Angle-Side (AAS) 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

Explain the HL postulate.

Back

The Hypotenuse-Leg (HL) 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 is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal. This property is fundamental in proving various geometric theorems.

Front

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

Back

To prove two triangles are congruent using the SSS postulate, you must show that all three corresponding sides of the triangles are equal in length.

Front

What information is needed to use the SAS postulate?

Back

To use the SAS postulate, you need to know the lengths of two sides and the measure of the included angle between those sides in both triangles.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent. Congruent triangles have equal corresponding sides and angles, while similar triangles have proportional sides and equal corresponding angles.

Front

How do you determine if two triangles are congruent using the AAS postulate?

Back

To determine if two triangles are congruent using the AAS postulate, you must show that two angles and a corresponding non-included side of one triangle are equal to two angles and the corresponding non-included side of the other triangle.