Triangle Congruence Shortcuts

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Triangle congruence means that two triangles are identical in shape and size, which can be proven using various congruence criteria.

'Cannot Be Determined' indicates that there is insufficient information to conclude that two triangles are congruent based on the given data.

The main triangle congruence criteria are: 1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side) 5. HL (Hypotenuse-Leg for right triangles).

SSS stands for Side-Side-Side, a criterion stating that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

ASA stands for Angle-Side-Angle, a criterion stating that 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.

HL stands for Hypotenuse-Leg, a criterion used for right triangles stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

To determine if two triangles are congruent using the AAS criterion, verify that two angles and the non-included side of one triangle are equal to the corresponding two angles and the non-included side of the other triangle.

Congruent triangles are important in geometry because they allow for the establishment of equal lengths and angles, which can be used to solve various geometric problems and proofs.