Congruent Triangles

Front

What is the definition of congruent triangles?

Back

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

Front

What does the SAS postulate state?

Back

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 does the ASA postulate state?

Back

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 does the AAS postulate state?

Back

If two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does the SSS postulate state?

Back

If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the HL postulate?

Back

The Hypotenuse-Leg postulate 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

If two triangles have one pair of equal angles and the sides opposite those angles are equal, what can be concluded?

Back

The triangles are congruent by the AAS postulate.

Front

What is the significance of a midpoint in triangle congruence?

Back

A midpoint divides a segment into two equal parts, which can be used to establish congruence between triangles.

Front

If two triangles share a side and have two angles equal, which postulate can be used to prove congruence?

Back

The ASA postulate.

Front

What is the relationship between the sides and angles in congruent triangles?

Back

In congruent triangles, corresponding sides are equal in length, and corresponding angles are equal in measure.