Congruent Triangles

Front

What does it mean for two triangles to be congruent?

Back

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

Front

What is the AAS congruence criterion?

Back

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

Front

What is the SSS congruence postulate?

Back

SSS stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the ASA congruence criterion?

Back

ASA stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What is the SSA condition and why is it not a valid congruence criterion?

Back

SSA stands for Side-Side-Angle, which is not a valid criterion for triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

What are corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that are equal in both triangles.

Front

What is the definition of a triangle?

Back

A triangle is a polygon with three edges and three vertices.

Front

What is the importance of congruence in geometry?

Back

Congruence is important in geometry because it allows us to determine that two shapes are identical in size and shape, which is essential for solving problems involving measurements and constructions.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are the same size and shape, while similarity means that triangles have the same shape but may differ in size.

Front

What is the definition of a postulate in geometry?

Back

A postulate is a statement that is accepted as true without proof and serves as a starting point for further reasoning and arguments.