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प्रश्न
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 ........................
विकल्प
parallelogram
rectangle
trapezium
MCQ
रिक्त स्थान भरें
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उत्तर
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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