Question

Suppose ABCD is a rhombus with AB = 12 inches. The midpoints of its sides are joined to form a quadrilateral. What type of quadrilateral is formed?

Answer 1

Answer:

A rectangle

Step-by-step 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