Question

a) yes; mnpl - ghjf because the corresponding angles are congruent; 2/5. b) yes; mnpl - ghjf because the corresponding angles are congruent and mn/gh = np/hj; 2/5. c) yes; mnpl - ghjf because the corresponding angles are congruent; 4. d) no; mn/gh ≠ np/hj

Explanation:

Step1: Check if corresponding angles are congruent

Both \(MNPL\) and \(GHJF\) are rectangles. In rectangles, all angles are \(90^{\circ}\). So, the corresponding angles of \(MNPL\) and \(GHJF\) are congruent.

Step2: Check the ratio of corresponding sides

For rectangle \(MNPL\), \(MN = 2\) and \(NP=4\). For rectangle \(GHJF\), \(GH = 8\) and \(HJ = 10\).
Calculate \(\frac{MN}{GH}=\frac{2}{8}=\frac{1}{4}\) and \(\frac{NP}{HJ}=\frac{4}{10}=\frac{2}{5}\). Since \(\frac{MN}{GH}
eq\frac{NP}{HJ}\), the rectangles are not similar.

Answer:

D. no; \(\frac{MN}{GH}
eq\frac{NP}{HJ}\)