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Question

If ABC and AMP are right triangles, right-angled at B and M respectively and MAP=BAC.

Prove that
(i) ABCAMP
(ii) CAPA=BCMP

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Solution

given that
ABC=AMP=90
and
MAP=BAC

therefore the other angle is also equal [since the sum of the angles must be 180]
since all the angles are equal the two triangles are similar

ABCAMP

therefore, as the two triangles are similar, the ratio of sides is the same
CAPA=BCMP

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