Congruent Triangles

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 congruent 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, a postulate that states if two angles and the included side of one triangle are congruent 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, a postulate that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What is CPCTC?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, a principle used to prove that corresponding sides and angles of congruent triangles are also congruent.

Front

Which postulate is invalid for proving triangle congruence?

Back

SSA (Side-Side-Angle) is not a valid postulate for proving triangle congruence.

Front

If ∆ABC≅∆XYZ, what can be concluded about sides AB and XY?

Back

AB≅XY, meaning side AB of triangle ABC is congruent to side XY of triangle XYZ.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that two shapes are identical in size and shape, which is fundamental in proofs and constructions.

Front

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

Back

To prove triangles are congruent using SAS, show that two sides of one triangle are equal to two sides of another triangle, and the angle between those sides is also equal.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side to be known, while AAS does not require the side to be between the two angles.