Question

In fig. BM & DN are both perpendicular to the segment AC &BM=DN.Prove that AC bisects BD. ​

Answer 1

$\huge{\pink{\red{\sf \boxed{Solution}}}}$

$\huge{\underline {\underline {\mathfrak{Given}}}}$

BM perpendicular to AC

DN perpendicular to AC

→BM=DN

$<p style="color:green;">To Prove:-</p>$AC bisects BD

Proof:-

In ∆ DON and ∆ BOM

DN=BM (given)

DON=BOM (Vertically opposite angle)

DNO=BMO ( each 90°)

∆DON congruent to ∆BOM(AAS criteria)

BO=DO (c.p.c.t)

so, AC bisects BD

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