How do you tell if triangles are congruent or not?

Answer 1

If they have the same sides and same angles then they are congruent.

Two triangles are called congruent if they have exactly the same size and shape. This can be determined by measuring all three sides of both triangles and measuring all three angles of both triangles.

The rules of geometry also tell us that we don't have to do all these measurement. Triangles have certain properties that simplify the matter. As an example, the sum of the internal angles of a triangle is 180 degrees. Therefore if two angles are known, the third angle is also known. Another is when three sides form a triangle, they only do so in one way so the angles between the sides can be determined.

There are specific rules for determining if two triangle are congruent:

• All three corresponding sides of both triangles are the same size.

• Two corresponding sides are the same length and the angle between them is the same

• Two corresponding angles are the same and the side between them is the same length

• Two angles are the same and the corresponding non-included side are equal.