Question

A transversal cuts two parallel lines at A and B. The two interior angles at A are bisected
and so are the two interior angles at B; the four bisectors form a quadrilateral ACBD.
Prove that
(1) ACBD is a rectangle.
(i) CD is parallel to the original parallel lines.
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Answer 1

Step-by-step explanation:

To prove → ABCD is a rectangle

AD, CD, AB, BC are bisectors of interior angles formed by transversal line with ∥ line.

∠BCA=∠CABHence,CB∥ABSimilarly,AB∥CB(∠CAB=∠ACB)(Alternateangles)

Therefore quadrilateral ABCD is a ∥gram as both the pairs of opposite sides are ∥

∠b+∠b+∠a+∠a=180∘⇒2(∠b+∠a)=180∘∠a+∠b=90∘

That is ABCD is ∥gram & one of the angle is ⊥ angle. 

So, ABCD is a Rectangle.

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