**Math Labs with Activity – Draw a Parallelogram Whose Two Adjacent Sides are-Given**

**OBJECTIVE**

To draw a parallelogram whose two adjacent sides are given, using the method of paper folding

**Materials Required**

- A sheet of white paper
- A geometry box

**Procedure**

**Step 1:** Take a sheet of white paper. Draw any two intersecting lines AB and BC which we have to use as two adjacent sides of a parallelogram (see Figure 14.1).

**Step 2:** Fold the paper along a line that cuts the line BC such that the part of the line BC that lies on one side of the line of fold falls on the other part. Make a crease and unfold the paper. Draw the line X_{1}Y_{1} along the crease as shown in Figure 14.2.

**Step 3:** Fold the paper along the line that passes through the point A and cuts the line X_{1}Y_{1}, such that the part of the line X_{1}Y_{1}, that lies on one side of the line of fold falls on the other part. Make a crease and unfold the paper. Draw the line X_{2}Y_{2} along the crease as shown in Figure 14.3. Then, the line X_{2}Y_{2} is parallel to the line BC.

**Step 4:** Produce the line AB to a point M. Fold the paper along a line that cuts the line AB (produced) such that the part of the line AB that lies on one side of the line of fold falls on the other part. Make a crease and unfold the paper. Draw the line X_{3}Y_{3 }along the crease as shown in Figure 14.4.

**Step 5:** Fold the paper along the line that passes through the point C and cuts the line X_{3}Y_{3} such that the part of the line X_{3}Y_{3 }that lies on one side of the line of fold falls on the other part. Make a crease and unfold the paper. Draw the line X_{4}Y_{4} along the crease as shown in Figure 14.5. Then, the line X_{4}Y_{4} is parallel to the line AB. Mark the point of intersection of the lines X_{2}Y_{2} and X_{4}Y_{4} as D. Join AD and CD by solid lines as shown in Figure 14.5.

**Observations**

Since AD is parallel to BC and DC is parallel to AB, ABCD is a parallelogram.

**Result**

ABCD is the required parallelogram having AB and BC as its two adjacent sides.

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