Five Reasons Why... Triangle Congruence

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side Side Side, which is 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

SAS stands for Side Angle Side, which is 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 ASA stand for in triangle congruence?

Back

ASA stands for Angle Side Angle, which is 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 AAS stand for in triangle congruence?

Back

AAS stands for Angle Angle Side, which is a theorem 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 does AAA stand for in triangle congruence?

Back

AAA stands for Angle Angle Angle, which is not a valid postulate for triangle congruence because it only proves that the triangles are similar, not congruent.

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

The 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 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

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important because it allows us to determine that two triangles are the same size and shape, which is fundamental in proving other geometric properties and theorems.

Front

Can two triangles be congruent if only two sides are known?

Back

No, two triangles cannot be proven congruent with only two sides known unless the included angle is also known (SAS). Otherwise, it may lead to ambiguous cases.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that triangles are the same size and shape, while similarity means that triangles have the same shape but may differ in size.