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Parallelograms — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsParallelograms3 Marks
Question
In the adjacent figure, ABCD is a rectangle. If BM and DN are perpendiculars from B and D on AC, prove that $\triangle\text{BMC}\cong\triangle\text{DNA}.$ Is it true that BM = DN?
✓

Answer

In $\triangle\text{BMC}$ and $\triangle\text{DNA}:$
$\angle\text{DNA}=\angle\text{BMC}=90^\circ$
$\angle\text{BCM}=\angle\text{DAN}$ (alternative angles)
BC = DA (opposite sides)
By AAS congruency criteria:
$\triangle\text{BMC}\cong\triangle\text{DNA}$ (proved)
So, we can write BM = DN.

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