How Many Criteria for the Congruence of the Triangle

Introduction:

The congruence of triangles is a property of two triangles. Any two triangles are said to be congruent if all three corresponding sides and angles of the triangles are equal. Read this entire article to learn about triangle congruence, the conditions under which two triangles are congruent, the corresponding parts of congruent triangles, and solved examples related to triangle congruence. Two shapes are said to be congruent if they are the same size and shape. The image of the two shapes should be the mirror image of one to match the other.

Congruent triangles are triangles that have the same size and shape. This means that corresponding sides are equal and corresponding angles are equal.

Congruent triangles do not have to have the same orientation or position. They must be the same size and shape.

Criteria for congruency of the triangle:

1. SSS (Side Side Side) Congruence Criteria (Condition):

Two triangles are congruent if three sides of one triangle are equal to three corresponding sides of the other triangle.

2. ASA (Angle Side Angle) Congruence Criterion (Condition):

Two triangles are congruent if the two angles and the included side of one are equal to the corresponding angle and side of the other.

3. AAS (Angle Angle Side) match criteria (condition):

Two triangles are congruent if they have two angles, each equal to the other two angles, and one side equal to the other's corresponding side.

4. SAS (Side Angle Side) Congruence Criteria (Condition):

Two triangles are congruent if two sides and included angles of a triangle are equal to the corresponding sides and included angles of another triangle. This congruence state is called azimuth side congruence. In short, write a SAS condition.

5. RHS (Right angle- Hypotenuse-Side) congruence criterion (condition):

Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other triangle.

Lastly, Things to Remember!

• Congruent triangles are triangles that have exactly the same sides and angles.

• There are four rules for determining whether two triangles are congruent. SSS, SAS, ASA, RHS

• The SSS congruence rule states that triangles are congruent if all their sides are equal.

• The SAS congruence rule states that two triangles are congruent if the two sides and the angle between the two sides are equal.

• The ASA congruence rule states that triangles are congruent if the two angles and the sides between the two angles are equal.

• The RHS rule states that two triangles are congruent if their hypotenuses and one side are equal in right triangles.