Question

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Answer 1

Now, since a perpendicular from D to AB bisects AB, D lies on perpendicular bisector of AB. Hence, it is equidistant from A and B.
$\to$ DA = DB. But, DB is a diagonal of Rhombus.
Further, since this is a Rhombus, DA = AB (all sides are equal in Rhombus)
$\to$ DA = DB = AB
$\to$ Triangle DAB is equilateral triangle
$\to$ Angle A = 60 degress.
Therefore angles of Rhombus are:
A = C = 60 degrees ; B = D = 120 degrees