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प्रश्न
Diagonals necessarily bisect opposite angles in a
विकल्प
rectangle
parallelogram
isosceles trapezium
square
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उत्तर
From the given choices, only in a square the diagonals bisect the opposite angles.
Let us prove it.
Take the following square ABCD with diagonal AD.
In ΔABD and ΔCBD:
AD = BC (Opposite sides of a square are equal.)
BD = BD (Common)
AB = DC (Opposite sides of a square are equal.)
Thus,
ΔABD ≅ ΔCBD (By SSS Congruence Rule)
By Corresponding parts of congruent triangles property we have:
∠ABD = ∠CBD
∠ADB = ∠CDB
Therefore, in a square the diagonals bisect the opposite angles.
Hence the correct choice is (d).
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