Question

these triangles are similar.
for each proportion listed below, determine whether or not it correctly represents the similarity relationship between the two figures.
select the correct option for each proportion.
\\( \frac { 45 } { 55 } = \frac { 9 } { 11 } \\)
\\( \frac { 45 } { 9 } = \frac { 55 } { 11 } \\)
\\( \frac { 55 } { 45 } = \frac { 45 } { 9 } \\)

Explanation:

Step1: Check the first proportion

For similar triangles, the ratios of corresponding sides are equal.
For \(\frac{45}{55}=\frac{9}{11}\), cross - multiply: \(45\times11 = 495\) and \(55\times9=495\).

Step2: Check the second proportion

For \(\frac{45}{9}=\frac{55}{11}\), cross - multiply: \(45\times11 = 495\) and \(9\times55 = 495\).

Step3: Check the third proportion

For \(\frac{55}{45}=\frac{45}{9}\), cross - multiply: \(55\times9=495\) and \(45\times45 = 2025\). Since \(495
eq2025\).

Answer:

• \(\frac{45}{55}=\frac{9}{11}\): Represents
• \(\frac{45}{9}=\frac{55}{11}\): Represents
• \(\frac{55}{45}=\frac{45}{9}\): Does Not Represent