Question

In the given below figure, AB = AC and CD
AC. Illustrate that BE bisects LABC

Answer 1

Answer:

ABCE is a quadrilateral in which AC is its diagonal and AB || EC, AB = AC

BA is produced to D

AE bisects ∠DAC

To prove:

(i) ∠EAC = ∠ACB

(ii) ABCE is a parallelogram

Proof:

(i) In ∆ABC and ∆ZAEC

AC=AC (common)

AB = CE (given)

∠BAC = ∠ACE (Alternate angle)

∆ABC = ∆AEC (SAS Axiom)

(ii) ∠BCA = ∠CAE (c.p.c.t.)

But these are alternate angles

AE || BC

But AB || EC (given)

∴ ABCD is a parallelogram