Triangles Congruence Theorem

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 ASA stand for in triangle congruence?

Back

Angle-Side-Angle; a method to prove triangles are congruent by showing two angles and the included side are equal.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side; a method to prove triangles are congruent by showing two angles and a non-included side are equal.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side; a method to prove triangles are congruent by showing two sides and the included angle are equal.

Front

What is a congruency statement?

Back

A statement that shows two triangles are congruent, typically written in the form ΔABC ≅ ΔDEF.

Front

What is the significance of the included angle in SAS?

Back

The included angle is the angle formed between the two sides being compared, which is crucial for establishing congruence.

Front

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

Back

No, at least two sides and the included angle (SAS) or two angles and a side (AAS or ASA) must be equal for congruence.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles to be equal, while AAS allows for a non-included side to be equal.

Front

What is the criteria for triangle congruence using SSS?

Back

Side-Side-Side; triangles are congruent if all three corresponding sides are equal.

Front

What is the importance of triangle congruence in geometry?

Back

It allows for the establishment of equality in shape and size, which is fundamental in proving other geometric properties.