Criteria for Congruence of Triangles Definition: Two triangles are congruent if they have the same shape and size, meaning their corresponding angles an...
Criteria for Congruence of Triangles
Definition: Two triangles are congruent if they have the same shape and size, meaning their corresponding angles and sides are equal.
Criteria for Congruence:
Corresponding angles: Corresponding angles are angles that are in the same position in the triangles. For example, if triangle A has angle A and triangle B has angle B, then angles A and B are congruent.
Corresponding sides: Corresponding sides are sides that are in the same position in the triangles. For example, if triangle A has side a and triangle B has side b, then sides a and b are congruent.
Angle measures: The sum of the angles in a triangle is always 180 degrees. If the sum of the angles in triangle A is equal to 180 degrees and the sum of the angles in triangle B is equal to 180 degrees, then the triangles are congruent.
Examples:
In triangle ABC, if angle A = 60 degrees and angle B = 30 degrees, then angles A and B are congruent.
In triangle DEF, if side a = 5 cm and side b = 12 cm, then sides a and b are congruent.
In triangle XYZ, if angle A = 40 degrees and angle C = 50 degrees, then angles A and C are congruent