Question

current skill $ rectangle pnjb is similar to rectangle hczt which proportion shows the similarity between these two figures?
\\( \frac { b j } { z t } = \frac { h c } { h t } \\)
\\( \frac { p n } { p b } = \frac { n p } { c h } \\)
\\( \frac { n p } { c h } = \frac { j b } { b p } \\)
\\( \frac { t z } { h t } = \frac { j b } { b p } \\)

Explanation:

Step1: Recall the property of similar rectangles

For similar rectangles, the ratios of corresponding sides are equal.

Step2: Analyze each option

• Option 1: \(\frac{BJ}{ZT}=\frac{HC}{HT}\), \(BJ\) and \(ZT\) are not corresponding sides, \(HC\) and \(HT\) are not corresponding sides.
• Option 2: \(\frac{PN}{PB}=\frac{NP}{CH}\), \(PN\) and \(NP\) are the same side, this is not a valid proportion for similar rectangles.
• Option 3: \(\frac{NP}{CH}=\frac{JB}{BP}\), \(NP\) and \(CH\) are corresponding sides, \(JB\) and \(BP\) are not corresponding sides.
• Option 4: \(\frac{TZ}{HT}=\frac{JB}{BP}\), \(TZ\) and \(JB\) are corresponding sides (widths of the rectangles), \(HT\) and \(BP\) are corresponding sides (lengths of the rectangles).

Answer:

\(\frac{TZ}{HT}=\frac{JB}{BP}\) (the fourth option)