Question

1. trapezoids defg and jklm are similar. which proportion must be true?

a $\frac{40}{30}=\frac{x}{8}$
b $\frac{40}{8}=\frac{x}{30}$
c $\frac{8}{40}=\frac{30}{x}$
d $\frac{8}{40}=\frac{x}{30}$
(there are two trapezoid figures: defg with de = 40 m, dg = 30 m; jklm with jk = 8 m, jm = x m)

Explanation:

Step1: Recall Similar Figures Property

For similar figures, corresponding sides are proportional. In trapezoids DEFG and JKLM, side DE (40 m) corresponds to side JK (8 m), and side DG (30 m) corresponds to side JM (x m).

Step2: Set Up Proportion

The ratio of corresponding sides should be equal. So, $\frac{\text{DE}}{\text{JK}}=\frac{\text{DG}}{\text{JM}}$, which is $\frac{40}{8}=\frac{30}{x}$ (or cross - multiplied form $\frac{8}{40}=\frac{x}{30}$). Let's check each option:

• Option A: $\frac{40}{30}=\frac{x}{8}$ → Corresponding sides not matched.
• Option B: $\frac{40}{8}=\frac{x}{30}$ → Incorrect correspondence (40 and 8 are one pair, 30 and x are another, but this ratio is reversed in terms of correspondence).
• Option C: $\frac{8}{40}=\frac{30}{x}$ → Incorrect correspondence.
• Option D: $\frac{8}{40}=\frac{x}{30}$ → Correct, as it follows the proportion of corresponding sides (JK/DE = JM/DG).

Answer:

D. $\boldsymbol{\frac{8}{40}=\frac{x}{30}}$