Triangle Congruence

Front

What is Triangle Congruence?

Back

Triangle Congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states 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

SAS stands for 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, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for 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, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, 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, the triangles are congruent.

Front

What is the HL theorem in triangle congruence?

Back

The HL theorem stands for Hypotenuse-Leg, which states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent.

Front

What is the difference between congruent triangles and similar triangles?

Back

Congruent triangles have the same size and shape (equal sides and angles), while similar triangles have the same shape but not necessarily the same size (proportional sides and equal angles).

Front

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

Back

To prove two triangles are congruent using the SSS postulate, measure all three sides of both triangles. If all three sides of one triangle are equal to the corresponding sides of the other triangle, they are congruent.

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which means if two triangles are congruent, you can use this property to find unknown lengths or angles.

Front

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

Back

No, knowing only one side is not sufficient to prove congruence. You need to know at least two sides and the included angle (SAS) or other combinations of sides and angles.