Congruence Statements

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, meaning they have the same shape and size.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What is the included angle in a triangle?

Back

The included angle in a triangle is the angle formed between two sides of the triangle.

Front

How do you denote the included angle between two sides?

Back

The included angle between two sides AB and AC is denoted as ∠BAC.

Front

What is the significance of the included side in a triangle?

Back

The included side is the side that connects two angles in a triangle and is crucial for determining congruence.

Front

If triangle ABC is congruent to triangle DEF, what can we say about their corresponding parts?

Back

If triangle ABC is congruent to triangle DEF, then AB = DE, BC = EF, AC = DF, ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.

Front

What is the relationship between congruence and transformations?

Back

Congruence can be established through transformations such as translations, rotations, and reflections, which do not change the size or shape of the figures.

Front

What is the Angle-Side-Angle (ASA) congruence criterion?

Back

The ASA criterion 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 is the Side-Angle-Side (SAS) congruence criterion?

Back

The SAS criterion 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.