Question

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

Answer 1

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