In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle is

In a equilateral triangle $ABC$, if $AD\perp BC$ then which of the following is true?

In a rhombus of side $10 \mathrm{cm}$, one of the diagonals is $12 \mathrm{cm}$ long. The length of the second diagonal is

In the given figure, $ABCD$ is a trapezium whose diagonals $AC$ and $BD$ intersect at $O$ such that $OA=\left(3x-1\right) \mathrm{cm}, OB=\left(2x+1\right) \mathrm{cm}, OC=\left(5x-3\right) \mathrm{cm}$ and $OD=\left(6x-5\right) \mathrm{cm}$. Then, $x=?$

The line segments joining the midpoints of the adjacent sides of a quadrilateral forms

If the bisector of an angle bisects the opposite side, then the triangle is 

In $∆ABC$, it is given that $\frac{AB}{AC}=\frac{BD}{DC}$. If $\angle B=70°$ and $\angle C=50°$, then $\angle BAD=?$