Construction of 5 Parallelograms
- Author:
- Megan Drake
Reasons why Constructions Work
1. With having both pairs of opposite sides parallel, it creates a parallelogram by ensuring the parallel characteristic. Also, by making it that both the pairs of opposite sides have to be parallel, it leads to having the lengths of the opposite sides to be congruent because where the lines would interest would cause them to form congruent lengths.
2. The diagonals bisecting each other forms a parallelogram because once you connect the endpoints of the diagonals, it forms the opposite sides being of congruent lengths and once you look further into it, the opposite sides are also parallel.
3. By creating a parallelogram with the lengths of the opposite sides congruent using circles in order to ensure the congruency of the lengths, it leads to the sides that are created also being parallel. Therefore, creating a parallelogram.
4. With the rotation of the triangle, it creates a parallelogram using the definition of the opposite angles being congruent, since when you rotate a triangle 180 degrees, it keeps the measures of the angles the same, therefore creating two sets of opposite angles that are congruent. Also, by rotating the triangle it keeps the side lengths congruent and parallel as well.
5. By starting with one set of sides parallel and congruent, it leads to forcing the other set of sides to be parallel and congruent when you connect the endpoints of the first constructed pair of sides.