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:
(i) ACBD is a rectangle.
(ii) CD is parallel to the original parallel lines.
​

Answer 1

Answer:

To prove → ABCD is a rectangle

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

∠BCA=∠CAB

Hence,CB∥AB

Similarly,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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