Chapter 6.6, Problem 62PPS

a.

To determine

To sketch:

Three quadrilaterals by using the given procedure

Answer to Problem 62PPS

Three quadrilaterals are drawn as:

  

Explanation of Solution

Given information:

  

Name of quadrilaterals: $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S},\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$

Sketch:

Construction steps:

• Draw a segment
• Construct a non congruent which bisects the first segment
• Form a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ by connecting the endpoints of segments

Here, draw quadrilaterals with the name $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S},\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$ .

  

b.

To determine

To calculate:

The measure values of each segments of quadrilaterals in the form of the table

Answer to Problem 62PPS

The measure values of each segments of quadrilaterals:

Figure	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$\mathrm{A}\mathrm{B}$	$0.8$	$\mathrm{B}\mathrm{C}$	$0.8$	$\mathrm{C}\mathrm{D}$	$1.6$	$\mathrm{D}\mathrm{A}$	$1.6$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$\mathrm{P}\mathrm{Q}$	$1.4$	$\mathrm{Q}\mathrm{R}$	$1.4$	$\mathrm{R}\mathrm{S}$	$1.8$	$\mathrm{S}\mathrm{P}$	$1.8$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$\mathrm{W}\mathrm{X}$	$0.4$	$\mathrm{X}\mathrm{Y}$	$0.4$	$\mathrm{Y}\mathrm{Z}$	$1.5$	$\mathrm{Z}\mathrm{W}$	$1.5$

Explanation of Solution

Given information:

  

Calculation:

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

Figure	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$\mathrm{A}\mathrm{B}$	$0.8$	$\mathrm{B}\mathrm{C}$	$0.8$	$\mathrm{C}\mathrm{D}$	$1.6$	$\mathrm{D}\mathrm{A}$	$1.6$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$\mathrm{P}\mathrm{Q}$	$1.4$	$\mathrm{Q}\mathrm{R}$	$1.4$	$\mathrm{R}\mathrm{S}$	$1.8$	$\mathrm{S}\mathrm{P}$	$1.8$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$\mathrm{W}\mathrm{X}$	$0.4$	$\mathrm{X}\mathrm{Y}$	$0.4$	$\mathrm{Y}\mathrm{Z}$	$1.5$	$\mathrm{Z}\mathrm{W}$	$1.5$

c.

To determine

To explain:

A conjecture about the quadrilateral’s diagonal

Answer to Problem 62PPS

A quadrilateral is kite.

Explanation of Solution

From the sub-part (b):

The length of quadrilateral’s diagonal are:

Figure	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)	Side	Length (cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$\mathrm{A}\mathrm{B}$	$0.8$	$\mathrm{B}\mathrm{C}$	$0.8$	$\mathrm{C}\mathrm{D}$	$1.6$	$\mathrm{D}\mathrm{A}$	$1.6$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$\mathrm{P}\mathrm{Q}$	$1.4$	$\mathrm{Q}\mathrm{R}$	$1.4$	$\mathrm{R}\mathrm{S}$	$1.8$	$\mathrm{S}\mathrm{P}$	$1.8$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$\mathrm{W}\mathrm{X}$	$0.4$	$\mathrm{X}\mathrm{Y}$	$0.4$	$\mathrm{Y}\mathrm{Z}$	$1.5$	$\mathrm{Z}\mathrm{W}$	$1.5$

From table:

Each kite has two pairs of congruent consecutive sides. If the diagonals of a quadrilateral are perpendicular, exactly one is bisected and the diagonals are not congruent, then it is defined as kite.