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प्रश्न
In a square ABCD, its diagonal AC and BD intersect each other at point O. The bisector of angle DAO meets BD at point M and bisector of angle ABD meets AC at N and AM at L. Show that - ∠ BAM = ∠ BMA
उत्तर
ABCD is a square whose diagonals AC and BD intersect each other at right angles at O.
∠ BAM = ∠ BAO + ∠ OAM
⇒ ∠ BAM = `45° + (45°)/2 = 67 (1°)/2`
And
⇒ ∠ BMA = 180° - (∠ AOM + ∠ OAM)
⇒ ∠ BMA = 180° - 90° - `(45°)/2 = 90° - (45°)/2 = 67(1°)/2`
∴ ∠ BAM = ∠ BMA
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