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I thought that you would have found post #2 particularly relevant.
In that case are we not assuming that A + B = 90degree ?
Well, yeah. But I would love to see any other proofs you have
Start with two right angled triangles, both with hypotenuse c. Let one have angle A and the other B.
Are you required to give a geometric proof?
What if they do not have?
They both have a side 'c'.
But the two right triangles are not congruent! You certainly cannot say that two right triangles containing equal angles are congruent.
Sin A=a/c and sin B=b/c then a=b ,so in two right triangles with angle A and B ,oposite side is a=b,hypottenuse is c,other side must be equal.thus two triangles are congruent,A=B
Draw right triangles ABC and PQR.
We know that Sin B = Sin Q so:
We can manipulate the above to
b / q = c / r = k
b = kq and c = kr
Pull the k^2 out to simplify.
ΔABC is similar to ΔPQR
B = Q
Provided that A and B are acute angles and sin A = sin B, prove that A = B