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?

Answer 1

Refer to the figure given in the book.

$$\begin{gathered} \mathrm{In}∆BMC\mathrm{and}∆DNA: \\ \angle DNA=\angle BMC=90° \\ \angle BCM=\angle DAN\left(\mathrm{alternate}\mathrm{angles}\right) \\ BC=DA\left(\mathrm{opposite}\mathrm{sides}\right) \\ By\mathrm{AAS}\mathrm{congruency}\mathrm{criteria}: \\ ∆BMC\cong ∆DNA \\ \mathrm{Yes},\mathrm{it}\mathrm{is}\mathrm{true}\mathrm{that}BMisequaltoDN.\left(by\mathrm{corresponding}\mathrm{parts}\mathrm{of}\mathrm{congruent}\mathrm{triangles}BMC\mathrm{and}DNA\right) \end{gathered}$$