Question

In the adjoining figure BM and DN are perpendiculars to AC such that BM=DN. Prove that AC bisects BD

Answer 1

See ∆DNP and ∆BMP,

DN=MB (given)
angle NPD = angle MPB (opposite angles)
angle DNP = angle BMP =90° (given perpendiculars)

So, ∆DNP and ∆BMP are congruent
Therefore, DP=PB

Answer 2

Step-by-step explanation:

Given: BM perpendicular to AC

DN perpendicular to AC

BM=DN

To prove: 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

Proved

hope this will help you!