SUBJECT: Geometry
GRADE: High School
TECHNOLOGY: Geometer’s Sketchpad
BY: Jacqueline Hayes

Discovering Properties of Parallel Lines

Target Grade/Subject: High School Geometry Class that has been studying geometry for at least two months and has previous course work in algebra. Lesson studied today will be used in future lessons in finding measurements of angles of various geometric figures and determining congruent angles.

Objective: Through use of Geometer’s Sketchpad, the student will discover properties of parallel lines cut by a transversal, including the congruence of corresponding angles, the congruence of alternate interior angles, and the supplementary property of same-side interior angles. Given two parallel lines cut by a transversal, the student will determine relationship between corresponding angles, alternate interior angles, and same-side interior angles nine out of ten times.

Materials:
Geometer’s Sketchpad program with enough computers for each student
Blackboard or dry erase board
Paper and pencil

Procedures:
* Each student will open Geometer’s Sketchpad program on computer
* Students will be told to construct one set of parallel lines or line segments using Sketchpad’s line creating button and parallel line option
* Students will next create a line or line segment that intersects both parallel lines
* Investigate measurement of all eight angles by highlighting three points of angle (with vertex point as second point) and using angle option
* Note on paper in which angles are congruent and which angles are supplementary
(see attached example of student output)
* Create a different line or line segment to cut the original two parallel lines
* Investigate measurement of eight new angles formed
* Again note on paper which angles are congruent and which angles are supplementary
* Repeat construction of parallel lines and transversal at least five more times
* Investigate measurement of all angles formed and note on paper
* During construction of angles with Sketchpad, teacher will circulate through room to make sure students are on-task and to offer assistance
* Hypothesize with partner on relationships between angles:
-which are congruent?
-which are supplementary?
* Write hypotheses on note paper to be handed in
* Teacher will circulate through room and check on groups to facilitate construction of the following theorems:
If two parallel lines are cut by a transversal,
1. then corresponding angles are congruent.
2. then alternate interior angles are congruent.
3. then same-side interior angles are supplementary.
* After appropriate time of hypothesizing, teacher will direct attention to the board
* Students will be encouraged to share their hypotheses
* Teacher will have example of parallel lines cut by a transversal on board with angles labeled for use in verifying or negating student responses
* Formal statement of theorems will be presented
* Two or three examples of stating which angles are congruent and which are supplementary will be done by teacher on board with student input
* Two or three examples of finding missing measurements of angles will be done on board
* Any questions will be answered
* Homework (practice problems from book) will be assigned

Evaluation:
Students will be assigned twenty homework problems from textbook and are expected to correctly answer 18 out of the 20. Teacher will circulate throughout room during activity in order to help students and make sure students are on-task.