Draw and describe the locus of a point in rhombus ABCD which is equidistant from AB and AD.
bisector of the angle between them.
Draw a rhombus ABCD. We know that the locus of a point equidistant from two intersecting lines is the bisector of the angle between them.
So, the locus of a point which is equidistant from AB and AD is the bisector of ∠BAD. Clearly, it coincides with the diagonal AC.