Question

in a quadrilateral ABCD if ∠b = 90
and ∠ACD = 90, then find AD² in terms of AB, BC & CD

Answer 1

hey

here is your answer

ABCD quadrilateral.    angle ABC = 90 deg.

              hence,  AB² + BC² = AC²     --- (1)    using Pythagoras theorem.

AD² = ( AB² + BC² ) + CD²  given,

    =  AC² + CD²          ---- (2)

In the triangle ACD,  AD has to be a hypotenuse and angle ACD must be 90 deg. as per Pythagoras theorem.

hope is help you

Answer 2

here is your answer OK dude


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Given: ABCD is a quadrilateral, ∠B = 90° and AD2 = AB2 + BC2 + CD2
To prove: ∠ACD = 90°
Proof: In right ∆ABC,
AC2 = AB2 + BC2 … (1)
Given, AD2 = AB2 + BC2 + CD2
⇒ AD2 = AC2 + CD2 (Using (1)
In ∆ACD,
AD2 = AC2 + CD2
∴ ∠ACD = 90° (Converse of Pythagoras theorem)

hope it help you