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

image with many line segments. 4 line segments join to form a rectangle. 1 line segment to create the diagonal of the rectangle. 2 more line segments connect to the bottom side of the rectangle to form a right triangle. 2 more line segments connect to the right side of the rectangle to form another right triangle.

1. Three lines on a field of dots intersect (cross) to form a triangle. Can you draw a fourth line so that the four lines form a quadrilateral?

   Use the drawing to explain or show your reasoning.

   

   dot paper drawing. Triangle created by 3 line segments. One horizontal line at the top. One vertical line on the right. One diagonal line from top left to bottom right.

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

   

   dot paper drawing. Triangle created by 3 line segments. One horizontal line at the top. One vertical line on the right. One diagonal line from top left to bottom right.

   Use the drawing to explain or show your reasoning.

3. Discuss the drawings with your group. Check if they agree with your conclusions.

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:

   1. Line H? If so, draw the line. If not, explain or show why it can’t be done.

   2. Line G? If so, draw the line. If not, explain or show why it can’t be done.

4. 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 would intersect neither Line H nor Line G? If so, draw the line. Explain how you know the lines would never cross. If not, explain why it can’t be done.