Free Lines Rays and Line Segments Worksheet | 10+ Pages - Free Printable

Let's analyze the given figure step by step and solve each part of the problem.

Given Figure:

The figure shows several lines, line segments, and rays intersecting at various points. The key points are labeled as \( A, B, C, D, E, N, \) and \( O \).

Solution:

#### i) Name the two intersecting lines?
- The two main intersecting lines in the figure are:
- Line \( AC \) (which extends through points \( A, O, \) and \( C \))
- Line \( BD \) (which extends through points \( B, O, \) and \( D \))

So, the two intersecting lines are:
\[
\boxed{AC \text{ and } BD}
\]

#### ii) How many line segments in the above figure?
- A line segment is a part of a line with two endpoints. Let's identify all the line segments:
- \( AO \)
- \( OB \)
- \( CO \)
- \( OD \)
- \( ON \)
- \( OE \)

There are 6 line segments in total.

So, the number of line segments is:
\[
\boxed{6}
\]

#### iii) Is there any parallel line, Name them
- Parallel lines are lines that never intersect and are always the same distance apart.
- In the figure, lines \( AC \) and \( BD \) are not parallel because they intersect at point \( O \).
- However, there are no other pairs of lines in the figure that are parallel.

So, there are no parallel lines in the figure:
\[
\boxed{\text{No parallel lines}}
\]

#### iv) Shortest line segment
- To determine the shortest line segment, we need to compare the lengths of all the line segments identified in part (ii):
- \( AO \)
- \( OB \)
- \( CO \)
- \( OD \)
- \( ON \)
- \( OE \)

From the figure, it appears that \( ON \) is the shortest line segment.

So, the shortest line segment is:
\[
\boxed{ON}
\]

#### v) ON is perpendicular to
- Perpendicular lines form right angles (90°) with each other.
- From the figure, it is clear that line segment \( ON \) is perpendicular to line \( BD \).

So, \( ON \) is perpendicular to:
\[
\boxed{BD}
\]

#### vi) How many rays are there in the above Figure?
- A ray starts at a point and extends infinitely in one direction.
- Let's identify all the rays in the figure:
- Ray starting from \( A \) and extending through \( O \) and beyond: \( \overrightarrow{AO} \)
- Ray starting from \( B \) and extending through \( O \) and beyond: \( \overrightarrow{BO} \)
- Ray starting from \( C \) and extending through \( O \) and beyond: \( \overrightarrow{CO} \)
- Ray starting from \( D \) and extending through \( O \) and beyond: \( \overrightarrow{DO} \)
- Ray starting from \( N \) and extending through \( O \) and beyond: \( \overrightarrow{NO} \)
- Ray starting from \( E \) and extending through \( O \) and beyond: \( \overrightarrow{EO} \)

There are 6 rays in total.

So, the number of rays is:
\[
\boxed{6}
\]

Final Answers:

1. \(\boxed{AC \text{ and } BD}\)
2. \(\boxed{6}\)
3. \(\boxed{\text{No parallel lines}}\)
4. \(\boxed{ON}\)
5. \(\boxed{BD}\)
6. \(\boxed{6}\)