Mathematics
Prove that bisectors of any two adjacent angles of a parallelogram are at right angles.
Rectilinear Figures
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Answer
Let AC be bisector of ∠A and BD be bisector of ∠B and they meet at point M.
From figure,
⇒ ∠A + ∠B = 180° (As AD || BC, sum of co-int ∠s = 180°)
⇒
⇒
∴ ∠MAB + ∠MBA = 90° …….(i)
In △MAB,
⇒ ∠MAB + ∠MBA + ∠AMB = 180° (Sum of angles of triangle = 180°)
⇒ 90° + ∠AMB = 180° (from i)
⇒ ∠AMB = 180° - 90°
⇒ ∠AMB = 90°.
Hence, proved that bisectors of any two adjacent angles of a parallelogram are at right angles.
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