Question

In the above isosceles triangle with AB = AC and X and Y as mid points of AB and AC respectively, then the relation between AX and YC is

• A. AX = 2YC
• B. $AX=\frac{1}{2}YC$
• C. $AX=\frac{2}{3}YC$
• D. AX = YC

Answer 1

The correct option is D AX = YC

As, X and Y are mid points of AB and AC respectively, we can say
$AX=BX=\frac{1}{2}AB\text{and}AY=YC=\frac{1}{2}AC$
and given that AB = AC,
So, $AX=\frac{1}{2}AB\text{and}YC=\frac{1}{2}AB$.

From Euclid's axioms, we know,
"Things that are equal to the same thing are equal to one another".
As, AX and YC are equal to the same thing i.e., $\frac{1}{2}$AB, clearly AX = YC .