in the figure CP is parallel to BD .it the area of traingle ABD is a and the area of traingle BCD is B complete the table
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Where is the figure dear?
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Q2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Sol: A parallelogram ABCD such that AC = BD In ΔABC and ΔDCB,
AC = DB
[Given]
AB = DC
[Opposite sides of a parallelogram]
BC = CB
[Common]
ΔABC = ΔDCB
[SSS criteria]
∴Their corresponding parts are equal.
⇒∠ABC = ∠DCB
...(1)
∵AB || DC and BC is a transversal.
[∵ ABCD is a parallelogram]
∴∠ABC + ∠DCB = 180°
...(2)
From (1) and (2), we have
∠ABC = ∠DCB = 90°
i.e. ABCD is parallelogram having an angle equal to 90°.
∴ABCD is a rectangle.
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