Question

If two medians of a triangle are equal, then the triangle is

• A. Equilateral
• B. Isosceles
• C. Scalene
• D. Right-angled

Answer 1

The correct option is B Isosceles

If $BE=CF$ and G is centroid, then
$GC=\frac{2}{3}FC=\frac{2}{3}BE=BG$
$FG=\frac{1}{3}FC=\frac{1}{3}BE=EG$
$\angle G=\angle G$
$\therefore \Delta FGB\cong \Delta EGC$ (By SAS postulate)
$\therefore FB=EC$
$or\frac{1}{2}AB=\frac{1}{2}ACorAB=AC$
Therefore, $\Delta ABC$ is isosceles.