Congruent Triangles

Front

What does congruent triangles mean?

Back

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

Front

What is the ASA postulate?

Back

The Angle-Side-Angle (ASA) 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 triangles are congruent.

Front

What is the SAS postulate?

Back

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

Front

What is the SSS postulate?

Back

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

Front

What is the AAS postulate?

Back

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

Front

What is the AAA criterion?

Back

The Angle-Angle-Angle (AAA) criterion states that if all three angles of one triangle are equal to all three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

What is the HL theorem?

Back

The Hypotenuse-Leg (HL) theorem 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 triangles are congruent.

Front

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

Back

To prove triangles congruent by HL, it is necessary to show that both triangles have a right angle.

Front

If two triangles have two sides equal and the included angle is not equal, are they congruent?

Back

No, the triangles are not congruent if the included angle is not equal, even if the two sides are equal.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which allows for the application of congruence postulates and theorems.