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Constructions
Question
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ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

Answer

Given: ABCD is a quadrilateral and BD is one of its diagonals.
To Prove: ABCD is a parallelogram and to determine its area.
Proof: ∠ABD = ∠BDC (= 90°) | Given But these angles form a pair of equal alternate
interior angles for lines AB, DC and a transversal BD AB || DC
Also, AD = DC (= 3 cm)    | Given
Hence, quadrilateral ABCD is a parallelogram. A quadrilateral is a parallelogram if its one pair of opposite sides are parallel and equal Now,
ar(||gm ABCD) = Base x corresponding altitude
= 3x4 = 12 cm2

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