**Math Labs with Activity – Verify that the Quadrilateral Formed by Joining the Midpoints**

**OBJECTIVE**

To verify that the quadrilateral formed by joining the midpoints of the sides of a quadrilateral is a parallelogram

**Materials Required**

- A sheet of white paper
- A sheet of glazed paper
- A geometry box
- A pair of scissors

**Procedure**

**Step 1:** Draw any quadrilateral ABCD on the white paper. Fold the paper so that point A falls on the point B. Make a crease and unfold the paper. Mark the point P where the line of fold cuts the side AB. Then, P is the midpoint of side AB of the quadrilateral. Similarly, find the midpoints Q, R and S of the sides BC, CD and DA respectively.

**Step 2:** Join the points P, Q, R and S to form the quadrilateral PQRS as shown in Figure 23.1.

**Step 3:** Make an exact copy of the quadrilateral PQRS on the glazed paper. Draw a diagonal by joining the points S and Q as shown in Figure 23.2.

**Step 4:** Cut ΔPQS. Rotate and place it over the ΔSQR as shown in Figure 23.3.

**Observations**

ΔPQS exactly covers ΔSQR.

Therefore, ΔPQS is congruent to ΔSQR and so, PQ = SR and PS = QR, i. e., two pairs of opposite sides are equal.

Hence, PQRS is a parallelogram.

**Result**

The quadrilateral formed by joining the midpoints of the sides of a quadrilateral is a parallelogram.

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