Explanation:

To understand why the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus, we need to consider the properties of a rectangle and the properties of a rhombus.

Properties of a Rectangle:
1. A rectangle has four right angles.
2. The opposite sides of a rectangle are equal in length.
3. The diagonals of a rectangle are equal in length and bisect each other.

Properties of a Rhombus:
1. A rhombus has four equal sides.
2. The opposite angles of a rhombus are equal.
3. The diagonals of a rhombus are perpendicular bisectors of each other.

Proof:

Let's consider a rectangle ABCD.

- Let E, F, G, and H be the midpoints of sides AB, BC, CD, and DA respectively.

Proof of Equal Sides:
- Since E is the midpoint of AB, AE=EB. Similarly, BF=FC, CG=GD, and DH=HA.
- Therefore, all four sides EF, FG, GH, and HE are equal.

Proof of Opposite Angles:
- Let's consider angle FGH.
- Since FG is parallel to CD and GH is parallel to AB, angle FGH is equal to angle CAD.
- Similarly, we can prove that angle HEF is equal to angle ABC, angle EFG is equal to angle BCD, and angle CGH is equal to angle CDA.
- Therefore, the opposite angles of the quadrilateral EFGH are equal.

Proof of Diagonals:
- Since E, F, G, and H are the midpoints of sides AB, BC, CD, and DA respectively, EF, FG, GH, and HE are parallel to the sides of the rectangle.
- Therefore, EF is parallel to GH and FG is parallel to HE.
- Also, EF is equal to GH and FG is equal to HE.
- Thus, the diagonals EF and GH of the quadrilateral EFGH are equal and bisect each other.

Since the quadrilateral EFGH has four equal sides, opposite angles are equal, and the diagonals bisect each other, it satisfies all the properties of a rhombus.

Therefore, the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus (Option B).

Option B is correct