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Parallelograms — MATHS STD 8 — Question

Gujarat 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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