In a quadrilateral abcd, angle a + angle d = 90°. prove that ac^2 + bd^2 = bc^2 + ad^2

Hence prove.

Step-by-step explanation:

Given:

∠A + ∠D = 90°

We are prove to that

Solution:

See required figure in attached file.

We know sum of the all angles of a triangle is 180°.

So, in triangle AED.

∠A + ∠E + ∠D = 180°

∠E + (∠A + ∠D) = 180°

Now, we substitute ∠A + ∠D = 90° in above equation.

∠E + 90° = 180°

∠E = 180° - 90°

∠E = 90°

Using Pythagoras Theorem for triangle ADE and triangle BEC.

Now, we add both above equations.

--------(1)

Similarly, Using Pythagoras Theorem for triangle AEC and triangle BED.

Now, we add both above equations.

--------(2)

We get From equation 1 and equation 2.

Hence prove,

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step-by-step explanation:

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