# Hi..!!What is the difference between RHS and ASA property.?

Hi!

Here is the answer to your query.

RHS congruence criterion

If under a correspondence, the hypotenuse and one side of a right triangle are respectively equal to the hypotenuse and one side of another triangle then the triangles are congruent.

Consider two right triangles ABC and DEF in which  ∠B = ∠E = 90°, AC = DF and BC = EF Here the hypotenuse of AC of right ΔABC is equal to the hypotenuse DF of right ΔDEF. One side BC of right ΔABC is equal to the side EF of right ΔDEF and ∠B = ∠E = 90°

∴  By RHS congruency criterion, we have ASA congruence criterion

If under a correspondence, two angles and the included side of a triangle are equal to two corresponding angles and the included side of another angle then the triangles are congruent. In ΔPQR and ΔXYZ

∠R = ∠Z

RP = XZ (Included side between two angles)

∠P = ∠X

So by ASA congruence criterion Cheers!

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RHS property- under a correspondence the hypotenuse should be equal and any 1 side of the 1st triangle should be equal to any 1 side of the 2nd triangle.

ASA property- under a correspondence the 2 angles and the included side should be equal to the 2 angles and the included side of the other angle.

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