Question

use what you know about similar figures to correct rene’s reasoning.
the side lengths of similar figures must also be proportional, which means that you can multiply or divide all the side lengths of one figure by the same number to get the corresponding side lengths of the other figure.

• pq × 1.2 = wx
• qr × = xy
• sr × = zy
• ps × = wz

Explanation:

Step1: Recall Proportionality

For similar figures, all corresponding sides are multiplied by the same scale factor. We know \( PQ \times 1.2 = WX \), so the scale factor is \( 1.2 \).

Step2: Analyze \( QR \) and \( XY \)

\( QR = 80 \, \text{cm} \), \( XY = 120 \, \text{cm} \). Let the scale factor be \( k \). Then \( QR \times k = XY \), so \( k=\frac{XY}{QR}=\frac{120}{80}=1.2 \).

Step3: Analyze \( SR \) and \( ZY \)

\( SR = 80 \, \text{cm} \), \( ZY = 96 \, \text{cm} \). Using the scale factor \( 1.2 \), \( 80\times1.2 = 96 \), so \( SR \times 1.2 = ZY \).

Step4: Analyze \( PS \) and \( WZ \)

\( PS = 80 \, \text{cm} \), \( WZ = 120 \, \text{cm} \). Using the scale factor \( 1.2 \), \( 80\times1.2 = 120 \), so \( PS \times 1.2 = WZ \).

Answer:

For \( QR \times \boldsymbol{1.2} = XY \), \( SR \times \boldsymbol{1.2} = ZY \), and \( PS \times \boldsymbol{1.2} = WZ \). The scale factor for all is \( 1.2 \).