GEOMETRIC REASONING - II

Midpoint Explorations

Task 1

Get a dot paper as shown below and draw different squares on it. Join the midpoints of the sides of each of these squares (in order) to create a new quadrilateral. The first one is shown as an example.

NOTE: The above activity can be done either on dot paper provided by the school or on GeoGebra software installed on your computer

Observe each of the new quadrilaterals formed, and complete the following:

The quadrilateral formed by joining the midpoints of sides of a square is a ________
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Suppose you were to join the midpoints of sides of a rectangle in a similar fashion. What shape do you think you might get? Think about it, and write your conjecture as below:
 

The quadrilateral formed by joining the midpoints of sides of a  
___________________________________ is a   _________________________________

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Explain why you think your conjecture is true (or false)
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Now verify your conjecture by drawing different rectangles on the dot paper below and joining the midpoints of the sides.

NOTE: The above activity can be done either on dot paper provided by the school or on GeoGebra software installed on your computer

Based on Task 3 does your conjecture hold? If not how would you modify it?

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Now make similar conjectures about other special quadrilaterals - rhombus and parallelogram,  and verify them. Write your conjectures in the space provided, and use the dot paper for verifying. 
 

NOTE: The above activity can be done either on dot paper provided by the school or on GeoGebra software installed on your computer.

Conjecture 1:
​______________________________________________________________________________ ______________________________________________________________________________

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Conjecture 2:
​______________________________________________________________________________ ______________________________________________________________________________

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Drawing on your observations in the previous five tasks, make a conjecture about the shape formed by joining the midpoints of sides of any quadrilateral.  Use the dot paper to verify. 
Conjecture :
____________________________________________________________ ____________________________________________________________ 
​​​​​
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If possible, draw a quadrilateral, joining whose midpoints of sides give a figure that is NOT a parallelogram. If not possible, explain why.
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