Congruent Triangles

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle: A postulate that states 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 SSS stand for in triangle congruence?

Back

Side-Side-Side: A postulate that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side: A postulate that states 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 AAS stand for in triangle congruence?

Back

Angle-Angle-Side: A postulate that states 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 definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

Can two triangles be congruent if only one side is known?

Back

No, at least two sides and the included angle or two angles and the included side must be known to determine congruence.

Front

What is the HL theorem in triangle congruence?

Back

Hypotenuse-Leg: A theorem that states 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 importance of triangle congruence in geometry?

Back

Triangle congruence helps in proving that two triangles are the same, which is essential for solving problems related to shapes, areas, and angles.

Front

If two triangles have two equal angles, what can be said about their sides?

Back

The sides opposite those angles are proportional, but the triangles may not be congruent unless a side is also known.

Front

What is an example of using the ASA postulate?

Back

If triangle ABC has angles A and B equal to angles D and E in triangle DEF, and side AB is equal to side DE, then triangle ABC is congruent to triangle DEF by ASA.