Question

. In triangle ABC, AC > AB and D is a point on AC such that AB = AD. Show BC > CD.

Answer 1

Answer:

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.

Step-by-step explanation:

Answer 2

In ∆ ABD, it is given that

AB = AD ….(i)  

In ∆ ABC, AB + BC > AC

 => AB + BC > AD + CD

 => AB + BC > AB + CD [∵AD = AB]

 => BC > CD