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Question
Complete the following statement by means of one of those given in brackets against each:
If one pair of opposite sides are equal and parallel, then the figure is ........................
Options
parallelogram
rectangle
trapezium
Solution
If one pair of opposite sides are equal and parallel, then the figure is parallelogram.
Reason:
In ΔABC and ΔCDA,
AB = DC Given)
AC = AC (Common)
∠BAC = ∠DCA (Because AB || CD, Alternate interior angles are equal)
So, by SAS Congruence rule, we have
ΔABC ≅ ΔCDA
Also,
∠BCA =∠DAC (Corresponding parts of congruent triangles are equal)
But, these are alternate interior angles, which are equal.
AD || BC
Thus, AB || CD and AD || BC
Hence, quadrilateral ABCD is parallelogram
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