The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a

Options

A. parallelogram
B. rectangle
C. rhombus
D. trapezium

Answer

To solve the question, we need to understand the properties of a quadrilateral and what happens when we join the midpoints of its adjacent sides. Here’s the step-by-step solution:

### Step 1: Understand the Quadrilateral
A quadrilateral is a four-sided polygon. It can have various shapes such as squares, rectangles, trapezoids, or irregular shapes.

**Hint:** Remember that a quadrilateral has four sides and four vertices.

### Step 2: Identify the Midpoints
For any quadrilateral, label the vertices as A, B, C, and D. The midpoints of the sides AB, BC, CD, and DA can be labeled as M, N, O, and P respectively.

**Hint:** The midpoint of a line segment is the point that divides it into two equal parts.

### Step 3: Join the Midpoints
Now, join the midpoints M and N (of sides AB and BC), N and O (of sides BC and CD), O and P (of sides CD and DA), and P and M (of sides DA and AB).

**Hint:** When you connect the midpoints of adjacent sides, you are creating a new shape.

### Step 4: Analyze the New Figure
The figure formed by joining the midpoints M, N, O, and P will always be a parallelogram. This is due to the properties of midsegments in a quadrilateral. Each pair of opposite sides of the new figure (the midpoints) will be equal and parallel.

**Hint:** Recall that in a parallelogram, opposite sides are equal and parallel.

### Step 5: Conclusion
Thus, we can conclude that the figure formed by joining the midpoints of the adjacent sides of a quadrilateral is a parallelogram.

**Final Answer:** The figure formed is a parallelogram.

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