Answer:
The first of the congruency theorems is
1) SSS :
Side-Side-Side or SSS is a kind of triangle congruence rule where it states that if all three sides of one triangle are equal to all three corresponding sides of another triangle, the two triangles are considered to be congruent. Two or more triangles are said to be congruent when the measurements of the corresponding sides and the corresponding angles are equal.
2) SAS:
SAS congruence is the term which is also known as Side Angle Side congruence, which is used to describe the relation of two figures that are congruent. Let's discuss the SAS congruence of triangles in detail to understand the meaning of SAS
Consider the two tringles blelow
Under this criterion, if the two sides of a triangle are equal to the two sides of another triangle, and the angle formed by these sides in the two triangles are equal, then these two triangles are congruent. The SAS Criterion stands for the 'Side-Angle-Side' triangle congruence theorem.
3) AAS:
The AAS Theorem says: If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Notice how it says "non-included side," meaning you take two consecutive angles and then move on to the next side (in either direction).
4) ASA:
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
5)HL:
The HL Theorem states; If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.