Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence 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 criterion for triangle congruence 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 criterion for triangle congruence 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 does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence 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 is the significance of congruent angles in triangle congruence?

Back

Congruent angles are significant in triangle congruence because they help establish relationships between triangles, allowing the use of congruence criteria like ASA and AAS to prove that triangles are congruent.

Front

What is the significance of congruent sides in triangle congruence?

Back

Congruent sides are significant in triangle congruence because they help establish relationships between triangles, allowing the use of congruence criteria like SSS and SAS to prove that triangles are congruent.

Front

What additional information is needed to prove two triangles are congruent by ASA?

Back

To prove two triangles are congruent by ASA, you need to know that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Front

What additional information is needed to prove two triangles are congruent by AAS?

Back

To prove two triangles are congruent by AAS, you need to know that two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

What additional information is needed to prove two triangles are congruent by SAS?

Back

To prove two triangles are congruent by SAS, you need to know that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Front

What is the relationship between triangle congruence and similarity?

Back

Triangle congruence means that two triangles are identical in shape and size, while triangle similarity means that two triangles have the same shape but may differ in size.