Question

1. □mabr~ □petu

scale factor: _
enlargement / reduction / ≅ /

1. △

pa
sca
enl

1. using example #6 determine

Explanation:

Step1: Find the ratio of corresponding sides

For similar polygons, the scale factor is the ratio of corresponding sides. Let's take \(MA = 40\) and \(TU=54\). The ratio is \(\frac{MA}{TU}=\frac{40}{54}=\frac{20}{27}\). Let's check with another pair of sides. Take \(AB = 35\). Assume the corresponding side is not clearly marked, but if we take \(MR = 20\) and \(TE = 42\), \(\frac{MR}{TE}=\frac{20}{42}=\frac{10}{21}\) (wrong). Wait, correct corresponding sides: Since \(MABR\sim PETU\), the order of similarity gives \(MA\) corresponds to \(TU\), \(AB\) corresponds to \(UP\), \(BR\) corresponds to \(PE\), \(RM\) corresponds to \(ET\). Let's take \(RM = 20\) and \(ET = 42\) (wrong). Wait, correct: \(\frac{MA}{TU}=\frac{40}{54}=\frac{20}{27}\), \(\frac{AB}{UP}=\frac{35}{24}\) (wrong). Wait, no, the scale factor is \(\frac{\text{length of side in }MABR}{\text{length of corresponding side in }PETU}\). Let's use \(MA = 40\) and \(TU = 54\), simplify \(\frac{40}{54}=\frac{20}{27}\). Check \(RM = 20\) and \(ET = 42\), \(\frac{20}{42}=\frac{10}{21}\) (error in problem? No, wait, the scale factor is consistent for all corresponding sides in similar polygons. Wait, actually, the problem might have a typo. Wait, correct approach: \(\text{Scale Factor}=\frac{\text{Length of side in first polygon}}{\text{Length of corresponding side in second polygon}}\). Let's assume \(MA\) corresponds to \(TU\). \(\frac{40}{54}=\frac{20}{27}\approx0.74\). Since \(\frac{20}{27}< 1\), it is a reduction.

Answer:

Scale Factor: \(\frac{20}{27}\), Reduction.