The relation of two objects being congruent is called congruence.
When two triangles have the same shape and size, or if one have the same shape and size as the mirror image of the other is known as congruent.
The symbol of Congruence is ≅.
If the figures cover each other completely, they are congruent. Alternatively, You may cut out one of them and place it over the other.
If two line segments have the same (i.e., equal) length, they are congruent. Also, if two line segments are congruent, they have the same length.
If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.
Two triangles are congruent if they are copies of each other and when superposed, they cover each other exactly.
Corresponding vertices : A and P, B and Q, C and R.
Corresponding sides : AB and PQ, BC and QR , AC and PR.
Corresponding angles : ∠A and ∠P, ∠B and ∠Q, ∠C and ∠R.
Criteria For Congruence of Triangles
If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
If you have two triangles drawn and want to verify if they are congruent, you cannot everytime cut out one of them and use method of superposition.
SSS Congruence criterion:
If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
If under a correspondence, two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.
Congruence in the case of two right triangles deserves special attention. In such triangles, obviously, the right angles are equal. So, the congruence criterion becomes easy.
Can you draw △ ABC with ∠B = 90°, if
RHS Congruence criterion:
If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.