Parallelogram Alec Contreras
Constructing a Paralellogram
1. Make segment AB
2. Select a point C and place it below the constructed segment
3. Select point C and segment AB and construct a parallel line with the options.
4. Make segment AC
5. Make a parallel line choosing point B and by selecting segment AC
6. Construct a segment CD and from point DB
Why this works:
The diagonals create angle bisectors and triangles that are congruent by the Angle Angle Angle postulate. Because we have congruent triangles we apply the rule of congruence for the opposite sides of the parallelogram going horizontally or vertically.
The opposite angles on the the parallelogram are congruent also and will continue to be no matter how much you move the vertices.
Degrees of freedom:
segment AC and segment BD, CD, CA, and BA
Vertices that can be manipulated: A,C and B