Question

D is any point on side ac of a triangle abc with ab=ac.Show that cd bd

Answer 1

In any Triangle, any single side is always less than the sum of other 2 sides. If this is not the case then we won’t have a Triangle.

Applying this logic, we know that ab + bc > ac (All these are lengths)

But ac is same as ad+dc (d is a point on ac, as given).

Therefore ab + bc > ad + dc, which is same as

ab + bc > ab + dc (since ad is same as ab, as given)

Subtracting ab from both sides, we get ab + bc - ab > ab + dc -ab

Cancelling ab on both sides, we get

bc > dc

Hence proved.

Hope it helps you