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?

image with many line segments.

Activity 1 Four Lines

  1. 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.

    dot paper drawing.
  2. 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.

    dot paper drawing.
  3. Discuss your drawings with your group. Check if they agree with your conclusions on both questions.

Activity 2 To Cross or Not to Cross

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

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

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

    3. 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.

    blank dot paper
  2. Here is a trapezoid.

    image of a 4 sided shape. Top side longer than bottom side. Top and bottom sides meet the left side at 90 degrees angles.

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

  3. 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.

dot paper drawing. 2 lines slanted at different angles.
  1. Explain why Andre is not correct.

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