Congruent Triangles

Front

What is the definition of 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 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 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 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 triangles are congruent.

Front

What is the definition of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that are in the same relative position in each triangle.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

If two triangles have two pairs of equal angles, the triangles are congruent by the AAS postulate.

Front

If two triangles have three pairs of equal sides, what can be concluded?

Back

If two triangles have three pairs of equal sides, the triangles are congruent by the SSS postulate.

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle in the SAS postulate is the angle formed between the two sides being compared, and it is crucial for establishing congruence.

Front

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

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or two angles and a side must be equal.