Criteria of Congruence

 

ABOUT:

Congruence Criteria

1. Side-Angle-Side (SAS):

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent.

Example:

If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.

2. Side- Side-Side (SSS):

If 3 sides in one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.

Example:

If in triangles ABC and DEF, AB = DE, BC = EF, and CA = FD, then triangle ABC is congruent to triangle DEF.

3. Angle-Side-Angle (ASA):

If two angle in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are congruent.

Example:

If in triangles ABC and DEF, angle A = angle D, angle B = angle E, and AB = DE, then triangle ABC is congruent to triangle DEF.

4. Side-Side-Angle (SSA):

Example:

In triangles ABC and DEF, angle A = angle D, AB = DE, and BC = EF. 

5. Hypotenuse-Leg (HL) for Right Triangles:

One case where SSA is valid, and that is when the angles are right angles. 

In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

Example:

If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.