Question

In a parallelogram ABCD the bisectors if A also bisects BC at x. If Ad =10cm, Find the value of AB.​

Answer 1

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Answer 2

Let

The b isectorof∠Ab isectsthesideBCatx.

Given;−ABCDisp a r a l l e o g r a m

∴AD∥BC

Now,AXisthetransversal

∴∠1=∠3(alternateangles)−−−−(1)

and∠1=∠2(AXistheb isectorof∠A)−−(2)

From(1)and(2)weget

∠1=∠3

Now,

InΔABX

∠1=∠3

⇒A B=BX

⇒2 A B=2BX=BX+BX=BX+XC(XisthemidpointsofBC)

⇒2 A B=BC

⇒2 A B=AD(oppositesideofaparallelogramareequal)

∴AD=2 A B

proved.