Parallelogram - Definitions and Constructions
- Author:
- Tibor Marcinek
- Topic:
- Constructions, Parallelogram, Quadrilaterals
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Our minimal definition:
Parallelogram – a quadrilateral with two pairs of parallel sides
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Construct a parallelogram. Then observe other constructions and answer the questions below.
Your construction:
What is the definition on which your construction is based?
Other parallelogram constructions
If you want to follow the construction steps, use the navigation buttons at the bottom to scroll through the steps. If you want to see the description/definition of an object, right click it (control+click on Mac).
Construction 1:
C1: What is the definition used in this construction?
Construction 2:
C2. What is the definition used in this construction?
Construction 3:
C3. What is the definition used in this construction?
++++++++++ Your own definition(s) ++++++++++++++
Before reading on, spend a few minutes playing with GeoGebra and try to come up with your own definition(s) of a parallelogram. For example, can you define prallelogram as a special case of trapezoid? etc. Is your definition valid? Is it minimal? Is it equivalent to our minimal definition?
Construction 4:
This is a "reverse" question. Given the definition below, decide if it is a valid definition of a parallelogram, equivalent to our minimal definition. You may want to construct it strictly from the definition and then play with your construction to formulate your conclusion.
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A trapezoid with congruent bases*.
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* Bases are the two sides of trapezoid that are parallel by the definition.
Your construction 4:
C4. Is this a valid definiton of a parallelogram, equivalent to our minimal definition?
Construction 5:
This is a "reverse" question. Given the definition below, decide if it is a valid definition of a parallelogram, equivalent to our minimal definition. You may want to construct it strictly from the definition and then play with your construction to formulate your conclusion.
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A quadrilateral with mutally bisecting diagonals.*
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* This means that diagonals intersect at their midpoints.
Your construction 5:
C5. Is this a valid definiton of a parallelogram, equivalent to our minimal definition?