Chapter 6.3, Problem 34PPS

To determine

To explain:

The method for the construction of parallelogram by using theorem 6.11

Answer to Problem 34PPS

The quadrilateral is a parallelogram if the quadrilateral’s diagonals bisect each other. First draw and bisect segment $\overline{\mathrm{A}\mathrm{B}}$ as

  

Explanation of Solution

As per the theorem 6.11:

The quadrilateral is a parallelogram if the quadrilateral’s diagonals bisect each other. First draw and bisect segment $\overline{\mathrm{A}\mathrm{B}}$ .

Then through the midpoint $\mathrm{D}$ draw a line which intersects the first drawn segment $\overline{\mathrm{A}\mathrm{B}}$ . Mark these points $\mathrm{C}$ and $\mathrm{D}$ on one and another side of line segment and then construct a congruent segment as $\overline{\mathrm{D}\mathrm{E}}$ and $\overline{\mathrm{C}\mathrm{D}}$ .

  

These are intersecting segments which are bisecting each other. Now, connect the remaining points as

• Point $\mathrm{A}$ to point $\mathrm{C}$
• Point $\mathrm{C}$ to point $\mathrm{B}$
• Point $\mathrm{B}$ to point $\mathrm{E}$
• Point $\mathrm{E}$ to point $\mathrm{A}$

Finally it forms the parallelogram $\mathrm{A}\mathrm{C}\mathrm{B}\mathrm{E}$ .