In the adjacent figure, ABCD is a rectangle. If BM and DN are perpendiculars from B and D on AC, prove that . Is it true that BM = DN?

Question

Philoid · Accepted Answer

In a triangles BMC and DNA
BC = DA (Opposite sides)
∠BCM = ∠DAN (alternate angles)
∠DNA = ∠BMC = 90° [DN and BM are perpendicular to AC]
So by AAS Congruency criterion
ΔBMC ≅ ΔDNA
BM = DN (By CPCT)