# Lesson 3 Two or More Lines

Let’s look at lines that cross and lines that don’t.

## Warm-up How Many Do You See: A Curious Figure

How many line segments do you see? How do you see them?

## Activity 1 Four Lines

Three lines on a field of dots

**intersect**(cross), forming a triangle. Can you draw a fourth line so that the four lines form a quadrilateral?Use the drawing to show your reasoning, or explain why it cannot be done.

Here is a copy of the same drawing. Can you draw a fourth line to form a rectangle?

Use the drawing to show your reasoning, or explain why it cannot be done.

Discuss your drawings with your group. Check if they agree with your conclusions on both questions.

## Activity 2 To Cross or Not to Cross

Here is another field of dots. Each dot represents a point.

Draw a line through at least 2 points. Label it line

. Draw another line that goes through at least 2 points and intersects your first line. Label it line

. Can you draw a new line that you think would never intersect:

line

? line

?

If so, draw the line. Be prepared to explain or show how you know the lines would never cross. If not, explain or show why it can’t be done.

Here is a trapezoid.

Do you think its top and bottom sides are parallel? What about its left and right sides? Explain or show how you know.

If you have time… Can you draw a new line that you think would never intersect either line

or line ? If so, draw the line and be prepared to explain or show how you know the lines would never cross. If not, explain why it can’t be done.

## Practice Problem

## Problem 1

Andre says that these two lines are parallel because they do not intersect.

Explain why Andre is not correct.

Draw a line that is parallel to one of the lines in the image.