Download Exploring Parallel Lines and Related Angles

Project AMP
Dr. Antonio Quesada – Director, Project AMP
Exploring Parallel Lines and Related Angles
Lesson Summary:
Students investigate the special angles formed by parallel lines.
Key Words:
parallel, transversal, alternate interior angles, exterior angles, same side interior
angles, supplementary angles, corresponding angles
Background Knowledge:
This lab is designed with the assumption that students know where to find most
tools and how to use them. A brief description of a tool and how to use it can be found
by selecting a tool and pressing F1. A help screen will appear across the bottom of the
screen and will describe each tool as it is selected. Further assistance and direction can
be found by referring to the instruction manual.
The extension activity has students write formal proofs of the theorems
discovered in this activity.
Learning Objectives:
Students will observe the relationship between the angles formed by two parallel
lines and a transversal.
Materials:
Geometry software such as Cabri Geometry
Suggested Procedure:
Split students into groups of two or three. Pass out worksheets and have students
complete the activity.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Exploring Parallel Lines and Related Angles
Team Members’ Names: _________________________________________________
File Name: _____________________________________________________________
Lab goals: Observe the relationship between the angles formed by two parallel lines and
a transversal.
1. Construct two parallel lines.
(use parallel tool)
2. Construct a point on each line. Label
them point A and B.
(point on object tool)
3. Construct a line through these two
points. This line is called a transversal.
A transversal is a line that intersects two
coplanar lines at two distinct points.
(line tool)
4. This is the time to investigate about
the angles. Label each of the eight
angles formed by the parallel lines and
transversal with the numbers 1 though
eight tool and measure each of them.
Write down the measurements of the
angles and your observations. What is
the relationship between the angles?
(comment tool, measure angle tool)
m∠1 =
m∠3 =
m∠5 =
m∠7 =
m∠2 =
m∠4 =
m∠6 =
m∠8 =
Observe the relationship between the angles formed by two lines and a transversal of
those two lines. Be able to identify alternate interior, same-side interior, exterior, and
corresponding angles.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
5. Open a new file. Create two lines
that are not parallel to each other and
label them l and m. Now make a third
line t that is a transversal to lines l and
m.
6. Label the points where the t intersects
lines l and m as points A and B. Again
there are eight angles formed by the
transversal and the two lines. Label
them with numbers 1 through 8.
(comment tool, angle measure tool)
7. Interior angles are those angles
formed by lines l and m and the segment
AB . Two interior angles, one having
vertex A and the other having vertex B,
whose interiors lie on opposite sides of t
are called alternate interior angle.
Name the pairs of alternate interior
angles of l and m.
8. Two interior angles, one having
vertex A and the other having vertex B,
whose interiors lie on the same side of t
are called same-side interior angles.
Name the pairs of same-side interior
angles of l and m.
9. Exterior angles are those angles
formed by the transversal t, the halfplain created by l that does not contain
line m, and the half-plain created by m
that does not contain line l. Name the
pairs of angles in the exterior of l and m.
10. Two angles are said to be
corresponding if both lie on the same
side of t and if ones orientation with
respect to line l is the same as the other’s
orientation with respect to m. Name all
the corresponding angles.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Extension Activity
Use the angles in the diagram for the following proofs.
11. Prove: If two parallel lines are cut
by a transversal, then alternate interior
angles are congruent.
Given: l || m
Prove: ∠3 ≅ ∠6
12. Prove: If two parallel lines are cut
by a transversal, then the pairs of same
side interior angles are supplementary.
Given: l || m
Prove: ∠3 and ∠5 are
supplementary.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Journal Activity
Exploring Parallel Lines and Related Angles
1. What was your favorite thing about this activity?
2. What was the most challenging thing?
3. What did you gain the most confidence about through completing this
lesson?
4. Where do you possibly see yourself using this knowledge in the future?