Question

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles


Please help me with proper written answer...i will mark you as brainliest....i promise....m waiting...do it as fast as you can!​

Answer 1

Now, in a parallelogram, we know that adjacent angles add up to 180

So, the sum of ∠A and ∠B (in the picture I attached) = 180

So, if we bisect ∠A into ∠a and ∠a, and ∠B into ∠b and ∠b
Then, 2∠a + 2∠b = 180
So, ∠a + ∠b = 90

Now, In △ABE, ∠a + ∠b + ∠AEB  = 180  (Angle Sum Theory)

But we know that ∠a + ∠b = 90

So,
∠AEB + 90 = 180
∠AEB = 180-90
∠AEB = 90

Hence proved

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