Parallelogram Explorations

Jim Doherty, Jan 28, 2016

This group of explorations look at the properties of parallelograms.

Table of Contents

  1. Parallelograms #1
    1. Parallelograms #1 - Parallel Sides
  2. Parallelograms #2
    1. Parallelograms #2 - Examining Interior Angles
  3. Parallelograms #3
    1. Parallelograms #3 - Relationship between Interior Angles
  4. Parallelograms #4
    1. Parallelograms #4 - Relationship between Diagonals

1.

Parallelograms #1

A sketch with opposite sides fixed parallel to each other.

  • 1. Parallelograms #1 - Parallel Sides

1.1.

Parallelograms #1 - Parallel Sides

In this sketch, the opposite sides of a quadrilateral are fixed as parallel to each other. You can see the slopes change as you manipulate the opposite vertices B and C.

What else would you like to know about this quadrilateral? Can you suggest any theorems of your own?
– Jim Doherty

2.

Parallelograms #2

In this worksheet we examine the relationship between interior angles in a parallelogram.

  • 1. Parallelograms #2 - Examining Interior Angles

2.1.

Parallelograms #2 - Examining Interior Angles

This time we are looking at angles rather than slopes - although we know the two are related. Again, you can manipulate by moving the opposite vertices C and B.

Observe what happens with the indicated angles. Why does this happen this way?
– Jim Doherty

3.

Parallelograms #3

In this worksheet we look at the interior angles of a parallelogram.

  • 1. Parallelograms #3 - Relationship between Interior Angles

3.1.

Parallelograms #3 - Relationship between Interior Angles

In this applet you can see what happens with the interior angles of a parallelogram. The opposite sides are parallel and you can manipulate this by changing vertex B or vertex C to see important relationships between the interior angles.
– Jim Doherty

4.

Parallelograms #4

In this worksheet we look at relationships between diagonals in a parallelogram.

  • 1. Parallelograms #4 - Relationship between Diagonals

4.1.

Parallelograms #4 - Relationship between Diagonals

In this applet you can see the lengths of the pieces of the diagonals from where they intersect to the vertex on the parallelogram.

It certainly appears that these diagonals meet at their midpoints. Can you prove that this must be true?
– Jim Doherty

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