Lesson 3 Two or More Lines

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

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

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.

Here is another field of dots. Each dot represents a point.
1. Draw a line through at least 2 points. Label it line $h$ .
2. Draw another line that goes through at least 2 points and intersects your first line. Label it line $g$ .
3. Can you draw a new line that you think would never intersect:
  - line $h$ ?
  - line $g$ ?
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 $h$ or line $g$ ? 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.

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