Question

Show that if the diagonals of a quadrilateral cut each other at right angle, then the sum of the squares of opposite sides are equal

Answer 1

AB² + CD² = BC² + DA² (Proved)

Step-by-step explanation:

See the attached diagram.

Given that, ∠ AOB = ∠ BOC = ∠ COD = ∠ DOA = 90° i.e. the diagonals of the quadrilateral ABCD, AC and BD intersect at right angle to each other.

We have to prove that, AB² + CD² = BC² + DA².

Now, from the right triangle Δ AOB, applying Pythagoras Theorem

AB² = AO² + BO² ............. (1)

Again, from the right triangle Δ COD, applying Pythagoras Theorem

CD² = CO² + DO² ............. (2)

So, from equations (1) and (2) we get,

AB² + CD² = AO² + BO² + CO² + DO² ............... (3)

Again, from the right triangle Δ BOC, applying Pythagoras Theorem

BC² = BO² + CO² ............. (4)

And, from the right triangle Δ DOA, applying Pythagoras Theorem

DA² = DO² + AO² ............. (5)

So, from equations (4) and (5) we get,

BC² + DA² = AO² + BO² + CO² + DO² ............... (6)

Therefore, from equations (3) and (6) we can write that

AB² + CD² = BC² + DA² (Proved)

Answer 2

Answer:

HEY MATE

Step-by-step explanation:

PLS PLS REFER TO THE ANSWER GIVEN IN ATTACHMENT . I HAVE EXPLAINED WITH ALL DETAILS.

1 IMP CONVENTION

P.T= PYTHAGORAS THEOREM.

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