Question

If in the below triangle $\angle B$ = 60${}^o$, which type of triangle is it and why?

Answer 1

From the figure, we can see that
BO is perpendicular to AC and AO = OC

$\because$ BO is cutting the base into half and is also perpendicular to it.
$\therefore$ BO is acting both as an altitude and median.

An altitude acts as a median only in an Equilateral or Isosceles triangle with AB and BC being equal in length.

For the triangle ABC,
Sum of all angles = 180${}^o$
Or, $\angle A$ + $\angle B$ + $\angle C$ = 180${}^o$
Or, $\angle A$ + $\angle C$ + 60${}^o$ = 180
Or, 2$\angle A$ = 180${}^o$ - 60${}^o$ ($\because$ angles opposite to equal sides are equal)
Or, $\angle A$ = $\frac{{120}^o}{2}$ = 60${}^o$

$\because$ $\angle A$ = $\angle B$ = $\angle C$ = 60${}^o$
$\therefore$ The above triangle is an Equilateral triangle.