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ABCD is a quadrilateral and BD is one of its diagonal as shown in the figure. Show that the quadrilateral ABCD is a parallelogram and find its area.
From figure, the transversal DB is intersecting a pair of lines DC and AB such that
∠CDB = ∠ABD = 90o.
Hence these angles from a pair of alternate equal angles.
DC ? AB.
Also DC = AB = 2.5 units.
Quadrilateral ABCD is a parallelogram.?
Now, area of parallelogram ABCD
= Base × Corresponding altitude
= 2.5 × 4
= 10 sq. units Ans.