Question

trapezoid nxqh is similar to trapezoid srgd
which proportion does not show the similarity between these two figures?
$$\frac { 21.7 } { 25.7 } = \frac { 13.02 } { 15.42 }$$
$$\frac { 13.02 } { 21.7 } = \frac { 15.42 } { 25.7 }$$
$$\frac { 13.02 } { 21.7 } = \frac { 21.7 } { 25.7 }$$
$$\frac { 21.7 } { 13.02 } = \frac { 25.7 } { 15.42 }$$

Explanation:

Step1: Recall the property of similar trapezoids

For similar trapezoids, the ratios of corresponding sides are equal. Let's assume \(NX = 15.42\), \(NH=13.02\), \(DS = 21.7\), \(SR = 25.7\). The ratios of corresponding sides should be \(\frac{NH}{DS}=\frac{NX}{SR}\) (since \(NH\) corresponds to \(DS\) and \(NX\) corresponds to \(SR\)).

Step2: Check each proportion

• Option 1: \(\frac{21.7}{25.7}=\frac{13.02}{15.42}\). Cross - multiply: \(21.7\times15.42=13.02\times25.7\). \(21.7\times15.42 = 21.7\times(15 + 0.42)=21.7\times15+21.7\times0.42=325.5+9.114 = 334.614\), \(13.02\times25.7=(13 + 0.02)\times25.7=13\times25.7+0.02\times25.7=334.1+0.514 = 334.614\).
• Option 2: \(\frac{13.02}{21.7}=\frac{15.42}{25.7}\). Cross - multiply: \(13.02\times25.7 = 21.7\times15.42\). As we calculated above \(13.02\times25.7=334.614\) and \(21.7\times15.42 = 334.614\).
• Option 3: \(\frac{13.02}{21.7}=\frac{21.7}{25.7}\). Cross - multiply: \(13.02\times25.7=21.7\times21.7\). \(13.02\times25.7 = 334.614\), \(21.7\times21.7=(20 + 1.7)\times(20+1.7)=400+2\times20\times1.7 + 2.89=400 + 68+2.89=470.89\).
• Option 4: \(\frac{21.7}{13.02}=\frac{25.7}{15.42}\). Cross - multiply: \(21.7\times15.42=13.02\times25.7\). As we calculated above \(21.7\times15.42 = 334.614\) and \(13.02\times25.7=334.614\).

Answer:

\(\frac{13.02}{21.7}=\frac{21.7}{25.7}\) (the third option) does not show the similarity between the two trapezoids.