ABCD is a parallelogram. The bisector of ∠A and ∠B meet at O. Line EF is drawn parallel to AB. Prove that AE = BF and O is midpoint of EF.
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closedIn the adjoining figure, ABCD is a parallelogram in which AB is produced to E so that BE = AB. Prove that ED bisects BC
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asked Dec 13, 2015 in Class IX Maths by anonymous
This is from chapter Quadrilaterals. Plz wrie everything given, To prove.
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answered Dec 13, 2015 by study_rankers Expert (1.5k points)
Given,
ABCD is a parallelogram.
BE = AB
To show,
ED bisects BC
Proof:
AB = BE (Given)
AB = CD (Opposite sides of ||gm)
∴ BE = CD
Let DE intersect BC at F.
Now,
In ΔCDO and ΔBEO,
∠DCO = ∠EBO (AE || CD)
∠DOC = ∠EOB (Vertically opposite angles)
BE = CD (Proved)
ΔCDO ≅ ΔBEO by AAS congruence condition.
Thus, BF = FC (by CPCT)
Therefore, ED bisects BC. Proved