Question

△abc and △def are similar.
(a) there are three proportions below. the ratios in each proportion compare the length of one of the sides of △abc to the length of the corresponding side of △def. complete the proportions.
\\(\frac{ab}{de} = \square\\) \\(\frac{ac}{\square} = \square\\) \\(\frac{bc}{\square} = \frac{3}{4}\\)
(b) choose the correct statement about the answers to part (a)

Explanation:

Step1: Find AB and DE lengths

AB = 12, DE = 16. So $\frac{AB}{DE} = \frac{12}{16} = \frac{3}{4}$.

Step2: Find AC and corresponding side

AC = 15, corresponding side in △DEF is DF = 20. So $\frac{AC}{DF} = \frac{15}{20} = \frac{3}{4}$.

Step3: Find BC and corresponding side

BC = 18, corresponding side in △DEF is EF = 24. So $\frac{BC}{EF} = \frac{18}{24} = \frac{3}{4}$.

For part (a):

• $\frac{AB}{DE} = \frac{12}{16} = \frac{3}{4}$
• $\frac{AC}{DF} = \frac{15}{20} = \frac{3}{4}$
• $\frac{BC}{EF} = \frac{18}{24} = \frac{3}{4}$ (matches $\frac{3}{4}$)

(Assuming part (b) is about the ratios being equal due to similarity, but since the question for (b) is cut off, focusing on (a) as per visible part.)

Answer:

For $\frac{AB}{DE}$: $\frac{3}{4}$; For $\frac{AC}{DF}$ (DF is the corresponding side), $\frac{3}{4}$; For $\frac{BC}{EF}$ (EF is the corresponding side), $\frac{3}{4}$ (filling the blanks: first blank $\frac{3}{4}$, second numerator AC, denominator DF, value $\frac{3}{4}$; third numerator BC, denominator EF).