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CBSE Class 9 Answered

Two parallel lines l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

l||m and p intersects them at points A and C respectively. Bisectors of interior angles intersect at B and D.

Now PAC = ACR (alternate angles)

AB||DC (as alternate angles are equal)

Similarly BC||AD

ABCD is a parallelogram

Also PAC + CAS = 180o (Linear pair)

ABCD is a ||gm with one angle 90o

ABCD is a rectangle.

Answered by | 04 Jun, 2014, 03:23: PM

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