Question

how to do congurence question easily

Answer 1

Two triangles are congruent if their corresponding sides are equal in length, in which case their corresponding angles are equal in measure.

In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.



Determining congruence

Sufficient evidence for congruence between two triangles in Euclidean space can be shown through the following comparisons:

SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.

SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. 
The ASA Postulate was contributed by Thales of Miletus (Greek). In most systems of axioms, the three criteria – SAS, SSS and ASA – are established as theorems. In the School Mathematics Study Group system SAS is taken as one of 22 postulates.

AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°. ASA and AAS are sometimes combined into a single condition, AAcorrS – any two angles and a corresponding side.

RHS (Right-angle-Hypotenuse-Side), also known as HL (Hypotenuse-Leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.