Chapter 6.5, Problem 45PPS

a.

To determine

To sketch:

Three kites withvarying sides and then draw the diagonals for each kite.

Answer to Problem 45PPS

Three kites with varying sides are drawn as:

  

Explanation of Solution

Given information:

  

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

Sketch:

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

. Then diagonals for each kite are drawn as below:

  

b.

To determine

To calculate:

The measure values of the diagonals of each kitein the form of the table.

Answer to Problem 45PPS

The measure values of the diagonals of each kite are:

Figure	Distance from $\mathrm{N}$to each vertex along shorter diagonal (cm)		Distance from $\mathrm{N}$to each vertex along longer diagonal(cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$0.8$	$0.8$	$0.9$	$1.5$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$1.2$	$1.2$	$0.3$	$0.9$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$0.2$	$0.2$	$1.1$	$0.4$

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	Distance from $\mathrm{N}$to each vertex along shorter diagonal (cm)		Distance from $\mathrm{N}$to each vertex along longer diagonal(cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$0.8$	$0.8$	$0.9$	$1.5$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$1.2$	$1.2$	$0.3$	$0.9$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$0.2$	$0.2$	$1.1$	$0.4$

c.

To determine

To explain:

A conjecture about the kite’sdiagonal.

Answer to Problem 45PPS

The shorter diagonals of a kite are bisected by the longer diagonals.

Explanation of Solution

From the sub-part (b):

The length of kite’s diagonal are:

Figure	Distance from $\mathrm{N}$to each vertex along shorter diagonal (cm)		Distance from $\mathrm{N}$to each vertex along longer diagonal(cm)
$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$	$0.8$	$0.8$	$0.9$	$1.5$
$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$	$1.2$	$1.2$	$0.3$	$0.9$
$\mathrm{W}\mathrm{X}\mathrm{Y}\mathrm{Z}$	$0.2$	$0.2$	$1.1$	$0.4$

Here, $\mathrm{N}$ is the midpoint of each short diagonal of the kite.

Therefore, the conjecture about the diagonals of the kite is:

The shorter diagonals of a kite are bisected by the longer diagonals.