Q4 of 40 Page 8

ABCD is a parallelogram AB is produced to E so that BE = AB. Show that ED bisects BC.

AB = BE    ..... (given)
Also AB = DC   ......(opposite sides of a parallelogram)
... BE = DC (Since AB = DC and AB = BE )
Since AE ïï DC and BC and DE are transversals,
... ∠1 = ∠2 and ∠3 = ∠4
(Alternate Interior angles of parallel sides)
Now in ΔBEP and ΔCDP,  
we have
        ∠2 = ∠1
        ∠3 = ∠4
and    BE = DC
ΔBEP ≅ ΔCDP    ...... (ASA Criterion)
... CP = PB        (c.p.c.t.)
... ED bisects BC at P.

More from this chapter

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2 If a diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angle and then the two diagonals are perpendicular to each other.
 3 In a ΔABC, lines are drawn through A, B and C parallel to sides BC, CA and AB respectively forming a triangle PQR. Prove that BC = QR.
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