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Q.

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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a

True

b

False

answer is A.

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Detailed Solution

In ΔBMC and ΔDNA,

∠DNA=∠BMC=90°

∠BCM=∠DAN    (Alternate angles)

BC=DA     (opposite sides)

By AAS congruency criteria:

ΔBMC≅ΔDNA

Yes, it is true that BM = DN.    (by corresponding parts of congruent triangles BMC and DNA)

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