Triangle Congruence Postulates

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 SSS stand for in triangle congruence?

Back

Side-Side-Side; a postulate stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side; a postulate stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle; a postulate stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side; a theorem stating 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, the triangles are congruent.

Front

What is the HL postulate?

Back

Hypotenuse-Leg; a postulate that states if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

Can two triangles be congruent if they have the same angles but different side lengths?

Back

No, triangles with the same angles must also have the same side lengths to be congruent (AAA does not prove congruence).

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence.

Front

How can you prove two triangles are congruent using the SSS postulate?

Back

By showing that all three corresponding sides of one triangle are equal to the three corresponding sides of another triangle.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.