Question

In the figure below, if AC$>$AB and D is point on AC such that AB = AD, then which of the following relation is true between BC and CD?

• A. BC > CD
• B. BC < CD
• C. BC $\le$ CD
• D. BC = CD

Answer 1

The correct option is A BC > CD

In $△$ABC,

Theorem: Sum of lengths of any two sides of a triangle is always more than the length of the third side.

On using the above theorem;

AB + BC $>$ AC

$\Rightarrow$ AB + BC $>$ AD + CD (Since AC = AD + DC)

$\Rightarrow$ AB + BC $>$ AB + CD (Since AB = AD)

$\Rightarrow$ BC $>$ CD