Congruent Triangles

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

It represents that two figures are congruent.

Front

What is the SAS postulate?

Back

The Side-Angle-Side (SAS) postulate 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 is the ASA postulate?

Back

The Angle-Side-Angle (ASA) postulate 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 AAS theorem?

Back

The Angle-Angle-Side (AAS) theorem states that if two angles and a 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 HL theorem?

Back

The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the difference between SSA and congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases, while other postulates like SAS, ASA, and AAS do guarantee congruence.

Front

How do you write a congruence statement for triangles?

Back

A congruence statement lists the corresponding vertices of the triangles in the same order, e.g., if ΔABC ≅ ΔXYZ, then A corresponds to X, B to Y, and C to Z.

Front

What is the importance of corresponding parts in congruent triangles?

Back

Corresponding parts of congruent triangles are equal, which allows us to make conclusions about the triangles' properties.

Front

What is the AAA criterion?

Back

The Angle-Angle-Angle (AAA) criterion states that if two triangles have equal corresponding angles, they are similar, but not necessarily congruent.