## Materials required:

Chart papers, pencil, compass, scale and a pair of scissors.

## Property 1:

A diagonal of a parallelogram divides it into two congruent triangles.

### As performed in real lab:

**Procedure:**

- Make a parallelogram on a chart paper and cut it.
- Draw diagonal of the parallelogram [Fig(a)].
- Cut along the diagonal and obtain two triangles.
- Superimpose one triangle onto the other [Fig(b)]

Fig (a) Fig (b)

Fig (c)

### As performed in the simulator:

- Select three points A, B and C anywhere on the workbench to draw a parallelogram.
- Now, click on any of the vertices to draw a diagonal. The diagonal divides the parallelogram into two triangles - a green colored triangle and blue colored triangle.
- Now, rotate the green triangle appropriately and drag to overlap blue triangle. Use rotation controls (r+ and r-) in "Tools" to rotate green triangle.
- See the observations and inference.

### Observations:

Two triangles are congruent to each other.

## Property 2:

Diagonals of a parallelogram bisect each other.

### As performed in real lab:

**Procedure:**

- Draw the parallelogram and its both diagonals.
- Cut the four triangles formed. Name them 1, 2, 3 and 4 [Fig(c)].
- Observe that triangle 2 is congruent to triangle 4 and triangle 1 is congruent to triangle 3 by superimposing them on each other.

### As performed in the simulator:

- Select three points A, B and C anywhere on the workbench to draw a parallelogram.
- Now, click on any two adjacent vertices to draw two diagonals. The diagonals divide the parallelogram into 4 triangles (two sets of opposite triangles)
- Click on "Next" to color the four triangles. One set of opposite triangle is colored blue and green, while other is colored brown and violet.
- Now, Rotate and Drag blue triangle over green triangle and brown triangle over violet triangle. Use rotation controls (r+ and r-) in "Tools" to rotate blue and brown triangles.
- See observations and inference.

### Observations:

- Base of triangle 2 = Base of triangle 4
- Base of triangle 1 = Base of triangle 3
- Thus the diagonals bisect each other.