Question

in a quadrilateral abcd,given that angle a + angle d =90.prove that ac²+bd²=ad²+bc²​

Answer 1

Answer:

Extend AB and CD to intersect at O

Now ∠AOD=90°  because given ∠A+∠D=90°

Applying right angled triangle rules ;

⇒AC2=OA2+OC2  and  ⇒BD2=OB2+OD2

Adding both equations ;

⇒AC2+BD2=(OA2+OD2)+(OB2+OC2)

⇒AC2+BD2=AD2+BC2

Step-by-step explanation: