Question

In the adjoining figure, BM ⊥ AC and DN ⊥ AC. If BM = DN, prove that AC bisects BD.

Answer 1

It is given that BM ⊥ AC and DN ⊥ AC

From the figure we know that ∠ DON and ∠ MOB are vertically opposite angles

∠ DON = ∠ MOB

Since DN and MB are perpendiculars

We know that

∠ DNO = ∠ BMO = 90^o

It is given that BM = DN

By AAS congruence criterion

△ DNO ≅ △ BMO

OD = OB (c. p. c. t)

Therefore, it is proved that AC bisects BD.