Question

δkgt ~ δnvm
which proportion does not show the similarity between these two figures?
\\( \frac { 21.42 } { 11.9 } = \frac { 21.78 } { 12.1 } \\)
\\( \frac { 11.9 } { 21.42 } = \frac { 12.1 } { 21.78 } \\)
\\( \frac { 11.9 } { 21.42 } = \frac { 21.78 } { 12.1 } \\)
\\( \frac { 12.1 } { 11.9 } = \frac { 21.78 } { 21.42 } \\)

Explanation:

Step1: Recall the property of similar triangles

For similar triangles \(\triangle KGT\sim\triangle NVM\), the ratios of corresponding sides are equal. That is \(\frac{KG}{NV}=\frac{KT}{NM}=\frac{GT}{VM}\)

Step2: Analyze each option

• Option 1: \(\frac{21.42}{11.9}=\frac{21.78}{12.1}\) can be rewritten as \(\frac{NM}{KT}=\frac{NV}{KG}\) (since \(NM = 21.42\), \(KT=11.9\), \(NV = 21.78\), \(KG = 12.1\)) which is a valid proportion for similar triangles.
• Option 2: \(\frac{11.9}{21.42}=\frac{12.1}{21.78}\) can be rewritten as \(\frac{KT}{NM}=\frac{KG}{NV}\) which is a valid proportion for similar triangles.
• Option 3: \(\frac{11.9}{21.42}=\frac{21.78}{12.1}\) implies \(\frac{KT}{NM}=\frac{NV}{KG}\). Cross - multiplying gives \(11.9\times12.1=21.42\times21.78\). \(11.9\times12.1 = 143.99\) and \(21.42\times21.78=466.5276\). They are not equal.
• Option 4: \(\frac{12.1}{11.9}=\frac{21.78}{21.42}\) can be rewritten as \(\frac{KG}{KT}=\frac{NV}{NM}\) which is a valid proportion for similar triangles.

Answer:

\(\frac{11.9}{21.42}=\frac{21.78}{12.1}\)