Question

based on the image, are triangles abc and xyz similar?
yes, because they are congruent
no, because the triangles are different sizes
yes, the side lengths are proportional
no, because only one side is the same
question 2
what does similarity require?

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(ABC\) with sides \(4\), \(6\), \(8\) and triangle \(XYZ\) with sides \(8\), \(12\), \(16\) (assuming the base of \(XYZ\) is \(16\) as per the proportion pattern).
The ratio of the first pair of sides: \(\frac{4}{8}=\frac{1}{2}\)
The ratio of the second pair of sides: \(\frac{6}{12}=\frac{1}{2}\)
The ratio of the third pair of sides: \(\frac{8}{16}=\frac{1}{2}\)

Step2: Check the similarity condition

Since the ratios of all corresponding sides \(\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}=\frac{1}{2}\), by the Side - Side - Side (SSS) similarity criterion, the triangles are similar.

Answer:

Yes, the side lengths are proportional.