Lab Manual: Quadrilateral Formed by Joining Mid-points of Sides of a Quadrilateral | Lab Manuals for Class 9 PDF Download

Objective

Prerequisite Knowledge
(i) Concept of finding mid-point of a line segment by performing paper folding activity.
(ii) Properties of a parallelogram.

Materials Required
Glazed papers, pencil, a pair of scissors, gluestick and tracing paper.

Procedure

• Take any coloured glazed paper.
• Draw a quadrilateral of any dimensions on glazed paper and name it as ABCD.
• Cut that quadrilateral from the glazed paper.
• Now, find the mid-point of each side AB, BC, CD, DA by paper folding and name them E, F, G, H respectively as shown infig. (i).
  
• Now, fold the figure along EF, GF, GH and EH. Press it and then unfold it as shown in fig. (ii).
  
• We will get creases along EF, GF, GH, HE.
• Make a replica (true copy) of EFGH (say PQRS) by using a tracing paper [fig.(iii)].
  
• Cut the quadrilateral PQRS along any diagonal (say RP) [fig.(iv)].
• We will get two triangles ∆PSR and ∆PQR.
• Now, overlap these two triangles. Two triangles coincide with each other [fig.(v)] such that side PS overlaps with QR and PQ with SR.
  

Observation
We observe that two triangles coincide with each other which means two triangles are congruent to each other. In a quadrilateral, two triangles cover each other completelv along any diagonal, then the quadrilateral will be a parallelogram.
∴ ∆PQR = ∆PSR
i.e., ar (∆PQR) = ar(∆PSR)
∴ PQRS is a parallelogram.

Result
As the replica of ∆PQR exactly covers the replica of ∆PSR
∴ PQ = RS, QR=SP
∴ PQRS is a parallelogram.

Learning Outcome
We have verified by paper folding that the quadrilateral formed by joining the mid-points of adjacent sides of a quadrilateral will be a parallelogram. We also learnt that a diagonal always divides the parallelogram into two triangles of equal areas.

Activity Time
What type of figures do you obtain?

• If you join mid-points of the sides of a rectangle (Do it by paper folding).
• If you join the mid-points of thesidesof a square (Do it by paper folding).