Answer:
A rectangle
Explanation:
The given parameters are;
The quadrilateral ABCD is a rhombus;
The length of the sides of the rhombus = 12 inches
The lengths of the sides of a rhombus are equal
The opposite interior angles of the rhombus are equal
The length of each midpoint from the vertex = 12 in./2 = 6 in.
Therefore, we have;
The line joining the midpoints form a quadrilateral with the length of the opposite sides equal
The sum of the interior angles of the rhombus = 180°
From the diagram created with Microsoft Visio, we have;
4·a + 4·b + 360 = 4 × 180 = 360 + 360
4·a + 4·b = 360
a + b = 90°
We have;
The interior angles of the quadrilateral formed = x
a + b + x = 180° Sum of angles on a straight line
∴ x = 180° - (a + b) = 180° - 90° = 90°
x = 90°
Therefore, the interior angles of the quadrilateral formed = 90°
The quadrilateral formed having equal opposite sides, and all interior angle of 90° each is a rectangle