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In triangle ABC, we are given that angle A =90. Median AM, angle bisector AK and the altitude AH are drawn. Prove that angle MAK = angle KAH

In triangle ABC,  we are given that angle A =90. Median AM, angle bisector AK and the altitude AH are drawn.  Prove that angle MAK = angle KAH

Grade:6

1 Answers

M
13 Points
3 years ago
Take vertical angle to be x(angle ABC)
since angle AHB is 90,BAH will be 90-x
but BAK is 45(angle bisector for 90)
so HAK is 45-90+x=x-45 -------1
HCA is 90-x(angle sum)
HAc will be x
but KAC is 45 (angle bisector)
so KAM is x-45--------2
from 1 and 2
KAM=KAH
 B|_C
 

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