Question

In quadrilateral abcd ab parallel to cd and de and ce bisect angle adc and bcd prove that ab is equal to sum of ad and bc

Answer 1

Answer:

In quadrilateral ABCD, we have AB=CD and AD=BC

⇒ Now, join segment AC.

⇒ In △ABC and △ACD, we have

⇒ AB = CD [Given]

⇒ AD = BC [Given]

⇒ AC = AC [Common side]

So, by SSS criteria,

⇒ △ABC≅△ACD

∴ ∠DAC = ∠BCA [By CPCT]

∴ CD∥AB [∵ Alternate angles are equal] ---- ( 1 )

⇒ ∠DCA=∠CAB [By CPCT]

∴ AD∥BC [∵ Alternate angles are equal] --- ( 2 )

From ( 1 ) and ( 2 ) we get that opposite sides of quadrilateral are parallel.

∴ ABCD is a parallelogram.