Question

if a line drawn parallel to base of isosceles triangle ito intersect its equal sides then prove that quadrilateral so formed is cyclic

Answer 1

We have
Since ABC is an isosceles triangle with AB = AC and DE is parallel to BC
So
angle ADE = angle ABC. __ corresponding angles
angle SVC = angel ACB____ (opposite angles of isoseleles triangle )

=>angle ADE = angle ACB

now,

angle ADE +angle EDB = 180°
angle ACB + angle EDB =180°

Thus the opposite angles of DECB are supplementary.

Hence DECB is a cylclic quadrilateral


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Answer 2

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