Congruent Triangles

Front

What are congruent triangles?

Back

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

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 is the significance of the HL theorem?

Back

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

Front

How can you determine if two triangles are congruent using transformations?

Back

Two triangles are congruent if one can be transformed into the other using a series of rigid transformations: translations, rotations, and reflections.

Front

What is the importance 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.

Front

What is the relationship between congruent triangles and geometric proofs?

Back

Congruent triangles are often used in geometric proofs to establish relationships between different figures and to prove theorems.

Front

What is the difference between congruence and similarity in triangles?

Back

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