Question

Determine if the line BC is parallel to line DE.

Known: BD = 1.5, DA= 2.5, and CE = 2.1 and EA = 3.5.
M
C
E
A-
B
O Yes, line BC is parallel to line DE because the proportions are not equal.
O Yes, line BC is parallel to line DE because the proportions are equal.
O No, line BC is not parallel to line DE because the proportions are not equal.
O No, line BC is not parallel to line DE because the proportions are equal.

Answer 1

After calculating and comparing the ratios BD/DA and CE/EA, both ratios equal 0.6, indicating that line BC is parallel to line DE because the proportions are equal.

Step-by-step explanation:

To determine if line BC is parallel to line DE, we need to use the information given, which includes the lengths BD, DA, CE, and EA. In similar triangles, corresponding sides are proportional. Therefore, we check if the sides in question, when divided, give the same ratio.

The lengths given are BD = 1.5, DA = 2.5, CE = 2.1, and EA = 3.5. We can form two ratios: BD/DA and CE/EA. After substituting the values, we get 1.5/2.5 and 2.1/3.5, which simplify to 0.6 and 0.6, respectively. Since both ratios are equal, we conclude that BC is parallel to DE. Thus, the correct option is: Yes, line BC is parallel to line DE because the proportions are equal.