Chapter 6.6, Problem 68HP

To determine

To sketch:

Two non-congruent trapezoids $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{F}\mathrm{G}\mathrm{H}\mathrm{J}$ .

Answer to Problem 68HP

Two non-congruent trapezoids $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{F}\mathrm{G}\mathrm{H}\mathrm{J}$ are

  

Explanation of Solution

Given information:

  $\overline{\mathrm{A}\mathrm{C}}\cong \overline{\mathrm{F}\mathrm{H}}$ and $\overline{\mathrm{A}\mathrm{C}}\cong \overline{\mathrm{F}\mathrm{H}}$

Sketch:

Know that:

Congruent trapezoids have corresponding sides and angles congruent. Diagonals $\mathrm{A}\mathrm{C}$ and $\mathrm{B}\mathrm{D}$ are drawn such that $\overline{\mathrm{A}\mathrm{B}}\parallel \overline{\mathrm{D}\mathrm{C}}$ .

Draw diagonals $\mathrm{F}\mathrm{H}$ and $\mathrm{G}\mathrm{J}$ which are of same length as $\mathrm{A}\mathrm{C}$ and $\mathrm{B}\mathrm{D}$ . If the diagonals are drawn such that the vertical angles are of different measure than those in $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ then $\mathrm{F}\mathrm{G}$ and $\mathrm{J}\mathrm{H}$ will be different than $\overline{\mathrm{A}\mathrm{B}}$ and $\overline{\mathrm{D}\mathrm{C}}$ .

Therefore, two non-congruent trapezoids $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{F}\mathrm{G}\mathrm{H}\mathrm{J}$

are drawn as: