Congruent Triangles

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SSS postulate state?

Back

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

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

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

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

Front

Is AAA a valid postulate for proving triangle congruence?

Back

No, AAA does not prove congruence; it only proves similarity.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Front

What is the importance of the included angle in SAS?

Back

The included angle is the angle between the two sides being compared; it is crucial for establishing congruence.

Front

Can two triangles be congruent if only one angle and two non-included sides are known?

Back

No, this does not provide enough information to prove congruence.

Front

What is the significance of the SSS postulate in triangle congruence?

Back

It is one of the most fundamental ways to prove that two triangles are congruent by comparing all three sides.