Question

In the given figure , BM and DN are perpendiculars to the line segment AC . If BM = DN , prove that AC bisects BD .​

Answer 1

$\underline \bold \red{ANSWER}$

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°

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.