Q8 of 24 Page 193

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?

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)


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