Question

matthew and luke are discussing the two triangles below. matthew says they are similar, due to their scale factor being 0.5. luke says that they are not similar. who is correct? matthew is correct. they are both incorrect since the sides have different scale factors. they are both correct because the different sides have different scale factors. luke is correct.

Explanation:

Step1: Calculate the scale factors for each pair of sides

For the sides \(35\) and \(21\): \(\frac{21}{35}=\frac{3}{5} = 0.6\)
For the sides \(25\) and \(15\): \(\frac{15}{25}=\frac{3}{5}= 0.6\)
For the sides \(20\) and \(12\): \(\frac{12}{20}=\frac{3}{5}= 0.6\)

Step2: Check similarity based on scale factors

Since the scale factor for all corresponding sides is the same (\(0.6\)), the triangles are similar.

Answer:

Matthew is correct.