Chapter 6.4, Problem 44PPS

a.

To determine

To sketch:

Three parallelograms with four congruent sides and then draw the two diagonals for each parallelograms

Answer to Problem 44PPS

Three parallelograms with four congruent sides are drawn as:

  

Explanation of Solution

Given information:

Name of parallelograms: $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P},\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$

Sketch:

Here, draw parallelograms with the name $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P},\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$

. Then two diagonals for each parallelograms are drawn as below:

  

b.

To determine

To calculate:

The measure values of the diagonals of each parallelograms in the form of the table

Answer to Problem 44PPS

The measure values of the diagonals of each parallelograms are:

Parallelogram	$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$		$\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P}$		$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$
Angle	$\angle \mathrm{A}\mathrm{R}\mathrm{B}$	$\angle \mathrm{B}\mathrm{R}\mathrm{C}$	$\angle \mathrm{M}\mathrm{N}\mathrm{R}$	$\angle \mathrm{N}\mathrm{R}\mathrm{O}$	$\angle \mathrm{W}\mathrm{R}\mathrm{X}$	$\angle \mathrm{X}\mathrm{R}\mathrm{Y}$
Angle Measure	$90°$	$90°$	$90°$	$90°$	$90°$	$90°$

Explanation of Solution

Given information:

  

Calculation:

To measure length of each diagonal of three parallelograms from subpart (a) need to use a protractor as:

Parallelogram	$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$		$\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P}$		$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$
Angle	$\angle \mathrm{A}\mathrm{R}\mathrm{B}$	$\angle \mathrm{B}\mathrm{R}\mathrm{C}$	$\angle \mathrm{M}\mathrm{N}\mathrm{R}$	$\angle \mathrm{N}\mathrm{R}\mathrm{O}$	$\angle \mathrm{W}\mathrm{R}\mathrm{X}$	$\angle \mathrm{X}\mathrm{R}\mathrm{Y}$
Angle Measure	$90°$	$90°$	$90°$	$90°$	$90°$	$90°$

c.

To determine

To explain:

A conjecture about the parallelogram’s diagonal with four congruent sides

Answer to Problem 44PPS

The diagonals of a parallelograms are congruent with four congruent sides are perpendicular.

Explanation of Solution

From the sub-part (a):

Three parallelograms are drwan as:

  

The lengths are caculated as:

Parallelogram	$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$		$\mathrm{M}\mathrm{N}\mathrm{O}\mathrm{P}$		$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$
Angle	$\angle \mathrm{A}\mathrm{R}\mathrm{B}$	$\angle \mathrm{B}\mathrm{R}\mathrm{C}$	$\angle \mathrm{M}\mathrm{N}\mathrm{R}$	$\angle \mathrm{N}\mathrm{R}\mathrm{O}$	$\angle \mathrm{W}\mathrm{R}\mathrm{X}$	$\angle \mathrm{X}\mathrm{R}\mathrm{Y}$
Angle Measure	$90°$	$90°$	$90°$	$90°$	$90°$	$90°$

The conjecture about the diagonals is:

The diagonals of a parallelograms are congruent with four congruent sides are perpendicular.