Mathematics
In the adjoining figure, ABCD is a parallelogram. If P and Q are mid-points of sides CD and BC respectively. Show that CR = AC.
Mid-point Theorem
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Answer
In parallelogram, diagonals bisect each other.
∴ AO = OC = AC ……(i)
In △BCD,
P and Q are midpoints of CD and BC,
PQ || BD (By midpoint theorem)
Since, PQ || BD
∴ QR || BO
In △BCO,
Q is midpoint of BC and QR || BO
∴ R is midpoint of OC
CR = OC
Substituting value of OC from (i) in above equation,
CR = OC = AC = AC.
Hence, proved that CR = AC.
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