Mid point of sides of a Quadrilateral forms parallelogram

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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 :

  1. Draw a quadrilateral ABCD
  2. Mark mid points on sides of the quadrilateral
  3. P is the midpoint of the side AB of the quadrilateral, similarly midpoints Q, R, S of the sides BC, CD and DA respectively
  4. Join the points P, Q, R and S form Quadrilateral PQRS
  5. If you join the mid-points of consecutive sides of a quadrilateral, what shape will you obtain?
  6. Measure sides of Quadrilateral PQRS?What is you conclusion?
  7. Identify and measure angles of the quadrilaterals PQRS? what is your conclusion?
  8. Identify pair of adjacent angles ? what is your conclusion?
  9. What type of figure is formed by joining the midpoints of a quadrilateral PQRS?
  10. 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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