Chapter 7.2, Problem 50PPS

(a)

To determine

To find: The measure for the three different sized square drawn.

Answer to Problem 50PPS

The square $ABCD,PQRS,WXYZ$ with the measure is shown in Figure 1, 2, 3.

Explanation of Solution

Given:

The label for the square is $ABCD,PQRS,WXYZ$ .

Calculation:

Consider the square $ABCD$ is shown in Figure 1

  

Figure 1

Consider the square $PQRS$ is shown in Figure 2

  

Figure 2

Consider the square $WXYZ$ is shown in Figure 3

  

Figure 3

(b)

To determine

To find: The ratio and record for the table with the ratio of the corresponding sides for the pair of the squares $ABCD-PQRS$ , $PQRS-WXYZ$ and $ABCD-WXYZ$ , then find if each of the pair is similar.

Answer to Problem 50PPS

The each pair of the square are similar.

Explanation of Solution

Consider the record shown in table for the pair ratio is shown in Table 1

Table 1

$ABCD,PQRS$	$PQRS,WXYZ$	$ABCD,WXYZ$
$AB:PQ$	$\frac{2}{3}$	$PQ:WX$	$\frac{3}{4}$	$WX:AB$	$2$
$BC:QR$	$\frac{2}{3}$	$QR:XY$	$\frac{3}{4}$	$XY:BC$	$2$
$CD:RS$	$\frac{2}{3}$	$RS:YZ$	$\frac{3}{4}$	$YZ:CD$	$2$
$AD:SP$	$\frac{2}{3}$	$SP:ZW$	$\frac{3}{4}$	$ZW:DA$	$2$

Thus the above table shows that each of the side pair are congruent as all the right angles are congruent and the corresponding side length are congruent.

Thus, each pair of the square are similar.

(c)

To determine

To find: The conjecture about the similarity of all the square.

Answer to Problem 50PPS

The each pair of the square are similar.

Explanation of Solution

The conjecture about the pair of square is all the angles of the squares are congruent and the ratio of the all the corresponding sides of the square are same. Thus, all the square are similar.

The each pair of the square are similar.