Question

Pls help me with this.
Prove that quadrilateral formed by the intersection of bisectors of interior angles made by a transversal on two parallel lines is a rectangle.

Answer 1

Answer:

Given:

Line l || Line m and Line p is the transversal  

To prove:

PQRS is a rectangle  

Proof:  

RS, PS, PQ and RQ are bisectors of interior angles formed by the transversal with the parallel lines.  

∠RSP = ∠RPQ (Alternate angles)  

Hence Rs || PQ

Similarly, PS||RQ (∠RPS = ∠PRQ)

Therefore quadrilateral PQRS is a parallelogram as both the pairs of opposite sides are parallel.

From the figure, we have

∠b + ∠b + ∠a + ∠a = 180°  

⇒ 2(∠b + ∠a) = 180°  

∴ ∠b + ∠a = 90°

That is PQRS is a parallelogram and one of the angle is a right angle.  

Hence PQRS is a rectangle

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