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In the adjoining figure, ABC is a triang...

In the adjoining figure, ABC is a triangle and D is any point in its interior. Show that `BD+DC lt AB +AC`.

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In `DeltaABE`,
`AB+AE gt BE`
`( :'" sum of two sides of atriangle is greater than the third side")`
`implies" "AB+AE gt BD+DE` ...(1)
In `DeltaCDE`,
`DE+EC gt DC` ...(2)
`( :'" sum of two sides of a triangle is greater than the third side")`
Adding (1) and (2), we get
`AB+AE+DE+EC gt BD+DE+DC`
`implies" "AB+(AE+EC) gt BD+DC`
`implies" "AB+AC gt BD+DC` Hence Proved.
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