Question

Angle bisector of A and B of a parallelogram meets on side CD at E if the perimeter of parallelogram is 30cm and length of bisector BE = 6 cm, the length of bisector AE =

Answer 1

Answer:

Given AB=20cm,AD=12cm

DC=AB=20cm and AD=BC=12cm

Given that bisector of ∠A intersects DC at E and BC produced at F.

Draw PF∥CD

From the figure, CD∥FP and CF∥DP

Hence PDCF is a parallelogram.

AB∥FP and AP∥BF

ABFP is also a parallelogram

Consider △APF and △ABF

∠APF=∠ABF [Since opposite angles of a parallelogram are equal]

AF=AF (Common side)

∠PAF=∠AFB (Alternate angles)

△PAF≅△BFA (By SAA congruence criterion)

AB=AP

AB=AD+DP

=AD+CF [Since DCFP is a parallelogram]

CF=AB−AD

=(20−12)cm=8cm