Question

lesson 12.1 checkpoint

1. find pn. round to the nearest tenth.
2. verify that the segments \\(wx\\) and \\(de\\) are parallel.

Explanation:

Identify the geometric relationship in Question 1

Using the Proportional Segments in Triangles knowledge point

$$
LATEXBLOCK0
$$

Substitute values and solve for PN

Using the Solving Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Verify parallel segments in Question 2

Using the Proportional Segments in Triangles knowledge point

$$
LATEXBLOCK2
$$

Apply the converse theorem

Using the Proportional Segments in Triangles knowledge point

$$
LATEXBLOCK3
$$

Answer:

Question 1

\(PN = 7.5\)

Question 2

Since the segments on the sides are proportional:

$$ \frac{FW}{WD} = \frac{1.5}{2.5} = 0.6 $$

$$ \frac{FX}{XE} = \frac{2.1}{3.5} = 0.6 $$

Because \(\frac{FW}{WD} = \frac{FX}{XE}\), by the Converse of the Triangle Proportionality Theorem, the segments \(WX\) and \(DE\) are parallel.