define sas,sss,rhs,asa?

ASA congruency is a rule which can be stated as:

Two triangles are said to be congruent, if two angles and the included side of one triangle are equal to the corresponding angles and the included side of the other triangle.

SAS congruency criterion can be stated as follows.

 “Two triangles are said to be congruent, if two sides and the included angle of a triangle are equal to the corresponding sides and the included angle of the other triangle”.

Consider the two triangles, ΔDEF and ΔXYZ, as shown in the following figure.

In these triangles,

And, ∠DEF = ∠XYZ

Thus, under the correspondence DEF ↔ XYZ, using SAS congruency criterion, we obtain

ΔDEF ≅ ΔXYZ

RHS congruence criterion:

 Two right-angled triangles are said to be congruent under a correspondence if the hypotenuse and one side of one right-angled triangle is equal to the hypotenuse and one side of the other right-angled triangle.

SSS congruence criterion:

Two triangles are said to be congruent under a correspondence if all the sides of one triangle is equal to all the corresponding sides of the other triangle.

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sas~side angle side

sss~side side side

asa~angle side angle

Rhs~right  hypotenuse  side

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