· Activity Name: Parallel Lines Cut by a Transversal

· Objectives:

Students will use their triangle page to identify Vertical, Corresponding, Alternate Interior and Alternate Exterior angles. The page can also be used to show parallel lines, transversals, acute or obtuse angles and triangles and their rotations and slides. Polygon angle sums can be shown, as well as the triangle angle sum and the exterior angle sum for all polygons.

· EALR/Standards:

1.3 understand and apply concepts and procedures from geometric sense.

2.1 investigate situations.

3.1 analyze information.

3.2 predict results and make inferences and make conjectures based on analysis of problem situations.

4.1 gather information.

4.2 organize and interpret information.

· Materials:

White Paper 8.5 X 11 (one sheet per student)

Scrap paper for students to cut triangles from (3X5 card per students is great)

Scissors

3 colored pens/pencils per group (red, green and blue is best)

Rulers

· Teacher Notes

o Prerequisites for the learner:

None

o Teacher hints for the activity:

Make sure that students color each corner of their triangle a different color and that as they trace they follow these rules: NEVER flip the triangle over; the colored corners should always be up. ALWAYS make sure that the vertices meet other vertices, there should never be a vertex touching a side. ALWAYS trace as accurately as possible, it is best if the vertices are dotted and then the ruler is used to connect the points. ALWAYS use a light pencil for drawing the triangles, this makes it easier to fix problems and it allows a darker marker to be used later to outline important patterns.

o Introductory questions:

**Do not give answers to these at the beginning. Simply let students think about them and work on them as they do the project.

If we want a triangle to be used as a base shape for tilling the plane, what type of triangle should we use?

What type of overall pattern will we get if we tile the plane with a triangle?

o Wrap-up questions:

What do you notice about Vertical, Corresponding, Alternate Interior and Exterior angles?

What is the sum of a red, blue and green angle?

What is the sum of triangles angles? How can this be shown?

How about the sum of other polygons?

What happens to the angle sum if the polygon is concave?

What is the exterior angle sum for a triangle? Other polygons?

o Solutions:

Introductory questions: Any triangle will tile the plane.

Parallel lines will develop.

Wrap-up questions: Congruent. Seen because they are the same colors.

180 degrees. Seen because they make a straight line.

180 degrees. Seen because they are one red, blue and green.

Draw a polygon and add up the red, blue and greens.

Does not change. Just draw and count the colors.

360 degrees. Seen by looking at the colors again.

o Assessment suggestions:

This activity is not really designed for assessing. Instead, it is best used as a note sheet designed for the students to see the different angles and sums. By allowing the students to write notes on the back, and drawing the shapes and angles on the front, it becomes a tool.

· The Activity:

Begin by having each student cut out a triangle. The triangle should have an area between 4 and 5 square inches. **This does not have to be perfect. It just helps those students who would otherwise cut out a tiny triangle and then get bored tracing it. It is great if some students use acute triangles and others obtuse triangles.

Next, each student needs to color the three corners a different color. The coloring should only be done on the corners not on the sides.

The third step is the tracing of the triangle onto the white paper. There are multiple ways of doing this. Here a couple of favorites:

1) Have each student start with the triangle in the lower left corner (one edge lined up with the paper’s edge, and one angle in the corner). Trace it and color the corners the same as the original. Next, slide the triangle to the right until the base is no longer overlapping. Trace the triangle again and color the corners. Do this all along the bottom edge. Once done with the bottom edge, rotate the triangle 180 degrees around the triangle’s left side so that it rests in-between two previously drawn triangles. When you color the corners, all three colors should meet at the bottom edge. Now slide the triangle left tracing and coloring. Continue sliding and rotating until the page is filled.

**Students should never flip the original triangle over. If a student sees a pattern developing and wants to use a ruler to finish the page, that is OK. Hopefully all students will see the pattern eventually and will use the rulers to make the page neat.

2) Have the students draw a line about 9 inches long somewhere on their papers. Place one side of the triangle along this line. Trace and color the corners. Slide the triangle along the line until the vertices meet (if side AB was on the line, slide along vector AB until vertex A is touching B). Trace and color again. Repeat this process until the triangle can no longer be slid along the line.

Rotate the triangle around the midpoint of the side against the line. Trace and color. At this point, vertices A and B of the newest triangle should be touching vertices B and A of an old triangle, and the original line should NOT be a reflecting line. Once again slide the triangle along the line, tracing and coloring until the triangle can no longer be slid along the line.

Rotate the triangle around a midpoint of a side. This should cause it to “fit” in between two previously draw triangles. The tracing should be the drawing of only one line. Trace and color. Slide the triangle between the next two previously drawn triangles, trace and color. Continue this until there are no more triangles to slide between.

Rotate the triangle around the midpoint of one side, trace and color. Slide the triangle along the rotated side, trace and color.

Continue rotating and sliding until the page is covered. As soon as a pattern is discovered, allow the students to use a ruler to finish the page instead of tracing.

3) Have the students place the triangle in the middle of the page. Trace carefully and color the corners. Next, rotate the triangle around a midpoint of a side. Trace and color again. Repeat the rotating, tracing, and coloring until the page is filled. It is VERY important that the tracing is done accurately. If a pattern is seen, allow the student to finish the page using the ruler instead of tracing every triangle.

**All vertices should meet. If a student does not have the vertices meeting (6 at a point), they will have to redo the work.