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Question

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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Solution

Refer to the figure given in the book.

In BMC and DNA:DNA=BMC=90°BCM=DAN alternate anglesBC=DA opposite sidesBy AAS congruency criteria: BMCDNAYes, it is true that BM is equal to DN. by corresponding parts of congruent triangles BMC and DNA

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