Here is the answer to your query.
Consider two ∆ABC and ∆PQR. In these two triangles ∠B = ∠Q = 90�, AB = PQ and AC = PR.
We can prove the R.H.S congruence rule i.e. to prove ∆ABC ≅ ∆PQR
We need the help of SSS congruence rule.
We have AB = PQ, and AC = PR
So, to prove ∆ABC ≅ ∆PQR in SSS congruence rule we just need to show BC = QR
Now, using Pythagoras theorems in ∆ABC and ∆PQR
Now, in ∆ABC and ∆PQR
AB = PQ, BC = QR, AC = PR
∴ ∆ABC ≅ ∆PQR [Using SSS congruence rule]
So, we have AB = PQ, AC = PR, ∠B = ∠Q = 90� and we have proved ∆ABC ≅ ∆PQR. This is proof of R.H.S. congruence rule.
Hope! This will help you.
Cheers!!!
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HL congruence theorem
reflexive property of congruence
True. Only if the given angle is between the two sides will the two triangles guarantee to be congruent (SAS), unless the given angle is a right angle (90°) in which case you now have RHS (Right-angle, Hypotenuse, Side) which does guarantee congruence.
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Reflecting