Question

in the figure ABCD is a parallelogram in which ab is produced to e so that a b equal to BC prove that ad bisects BC and if ad is equal to 10 cm find AB​

Answer 1

Answer:

Given : ABCD is a parallelogram

            BE=AB

To prove : ED bisects AB

Proof :

AB=BE (given)

AB=CD (opposite sides of a parallelogram

therefore   BE=CD⟶(1)

Let DE intersects BC at F

Now in ΔCDF & ΔBEF

∠DCF=∠EBF   (∵   AB∥CD)

∠DFC=∠EFB      (vertically opposite angles)

BE=CD    (proved in equation (1)

Thus BF=FC    (by CPCT)

Thus, ED bisect BC

                                Hence proved.

Step-by-step explanation:

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