# Mid point of sides of a Quadrilateral forms parallelogram

From Karnataka Open Educational Resources

## Contents

### Objectives

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

### Estimated Time

20 minutes

### Prerequisites/Instructions, prior preparations, if any

Knowledge about adjacent angles, quadrilaterals, parallelogram

### Materials/ Resources needed

Digital:Click here to open the file

Non-digital:paper, pencil, ruler, compass,

### Process (How to do the activity)

Download this geogebra file from this link.

**Procedure** :

- Draw a quadrilateral ABCD
- Mark mid points on sides of the quadrilateral
- P is the midpoint of the side AB of the quadrilateral, similarly midpoints Q, R, S of the sides BC, CD and DA respectively
- Join the points P, Q, R and S form Quadrilateral PQRS
- If you join the mid-points of consecutive sides of a quadrilateral, what shape will you obtain?
- Measure sides of Quadrilateral PQRS?What is you conclusion?
- Identify and measure angles of the quadrilaterals PQRS? what is your conclusion?
- Identify pair of adjacent angles ? what is your conclusion?
- What type of figure is formed by joining the midpoints of a quadrilateral PQRS?
- What are the main properties of a parallelogram?

### Evaluation at the end of the activity

What type of figure is formed by joining the midpoints of a parallelogram?

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