Congruent Triangles Flashcard

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 all corresponding sides and angles are equal.

Front

What is the ASA postulate in triangle congruence?

Back

The ASA (Angle-Side-Angle) 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 postulate in triangle congruence?

Back

The AAS (Angle-Angle-Side) postulate 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 Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning for any triangle ∆ABC, ∆ABC ≅ ∆ABC.

Front

What does the HL theorem state regarding triangle congruence?

Back

The HL (Hypotenuse-Leg) 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 are the three main criteria for triangle congruence?

Back

The three main criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle).

Front

What is the SSS postulate in triangle congruence?

Back

The SSS (Side-Side-Side) postulate 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 SAS postulate in triangle congruence?

Back

The SAS (Side-Angle-Side) 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

How can you prove that two triangles are congruent using the properties of angles?

Back

You can prove two triangles are congruent by showing that all corresponding angles are equal, which can be done using the AA (Angle-Angle) similarity criterion.

Front

What is the significance of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are equal, which means that if two triangles are proven to be congruent, all their corresponding sides and angles are also equal.