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

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

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In a triangles BMC and DNABC 

= 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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