Question

1. the diagram below is the side view of a bookshelf with only one shelf shown. is the shelf along km parallel to the floor jn? explain.

28 in.
36 in.
21 in.
30 in.

Explanation:

Step1: Check side - length ratios

We use the converse of the Basic Proportionality Theorem. Calculate the ratios of the corresponding sides of the two triangles formed. The two triangles are $\triangle LKM$ and $\triangle LJN$. The ratio of the left - hand sides is $\frac{LK}{LJ}=\frac{28}{28 + 21}=\frac{28}{49}=\frac{4}{7}$. The ratio of the right - hand sides is $\frac{LM}{LN}=\frac{36}{36+30}=\frac{36}{66}=\frac{6}{11}$.

Step2: Compare ratios

Since $\frac{4}{7}
eq\frac{6}{11}$, by the converse of the Basic Proportionality Theorem (if a line divides two sides of a triangle proportionally, then it is parallel to the third side), the line segment $KM$ is not parallel to the line segment $JN$.

Answer:

No, the shelf along $\overline{KM}$ is not parallel to the floor $\overline{JN}$ because the ratios of the corresponding sides of the two triangles formed are not equal.