Congruent Triangle Proofs

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, which means their corresponding sides and angles are equal.

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, segment AB is congruent to segment AB.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the significance of the statement 'MN ≌ ON'?

Back

The statement 'MN ≌ ON' indicates that segment MN is congruent to segment ON, which is a key piece of information in proving triangle congruence.

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 geometric statement or theorem.

Front

What is the definition of congruence in geometry?

Back

Congruence in geometry refers to the property of figures having the same shape and size, allowing them to be superimposed on one another.

Front

What is the importance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which is essential for establishing triangle congruence.

Front

What is the difference between a theorem and a postulate?

Back

A theorem is a statement that has been proven based on previously established statements, while a postulate is a statement accepted as true without proof.

Front

What is the role of the included angle in the SAS congruence criterion?

Back

The included angle in the SAS criterion is the angle formed between the two sides being compared; it must be congruent for the triangles to be proven congruent.