PROOFS with Congruent triangles

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is considered, then triangle ABC ≅ triangle ABC.

Front

Which triangle congruence criteria is not valid?

Back

SSA (Side-Side-Angle) is not a valid criterion for proving triangle congruence.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion used to prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What is the SAS criterion in triangle congruence?

Back

SAS stands for Side-Angle-Side, which 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 statement ∆GFH≅∆IFH indicate?

Back

It indicates that triangle GFH is congruent to triangle IFH, which is a conclusion drawn in a proof.

Front

What is the significance of congruent triangles in proofs?

Back

Congruent triangles are significant in proofs because they allow us to establish that certain properties, lengths, and angles are equal, which can be used to solve problems or prove further statements.

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry means that two figures have the same shape and size, and can be superimposed onto each other.

Front

What is the importance of the Angle-Angle-Angle (AAA) criterion?

Back

While AAA can show that two triangles are similar, it does not prove congruence because it does not provide information about the lengths of the sides.

Front

What is the purpose of a proof in geometry?

Back

The purpose of a proof in geometry is to provide a logical argument that demonstrates the truth of a statement or theorem based on previously established facts and definitions.

Front

What does the term 'included angle' refer to in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle. It is crucial in the ASA and SAS criteria for triangle congruence.