The Geometry of a Circle - By: Dennis Kapatos

Lesson 5: Angles Formed by Chords and Secants
Coordinate Graphing with GSP – Using Graphs to Determine Geometric Relationships
Materials and Handouts:
Teacher’s Computer with GSP
Projector
Student’s Computers with GSP
GSP Worksheet Files
Textbooks
Graphing Calculators
Name: Dennis Kapatos
Grade: 11
Subject: Geometry
Lesson Objectives:
● Students will be able to write/describe and prove Theorem 12.12 and 12.13.
● Students will be able to recognize real world applications of circles and the theorems
learned so far.
● Students will be able to use coordinate graphs to determine the relationship between parts
of geometric figure.
● Students will be able to work cooperatively to prove geometric theorems.
● Given a geometric figure with missing measurements, students will be able to apply the
theorems learned so far to find them.
Reviewing Homework:
1. Answers to the homework questions 1-12, 15, 16, 24-27, and 28 will be shown with the
projector. Students will correct their own homework.
2. Teacher will ask each student to share the real life applications they have come up with using
the projector to show their drawings etc..
Anticipatory Set:
3. Students will look at the sketches they made on GSP from lesson and teacher will ask questions
to help them remember what theorems they learned.
Developmental Activity:
4. Students will still be on GSP.
5. Teacher will talk the students through how to create the drawing using the teacher’s
instructions below. Teacher will ask questions when indicated. Theorems will be conjectured and
entered into notes as the discussions progress.
6. At the end of the teacher’s instructions, the students will work in pairs to try to prove Theorem
12.13. Teacher will help them though they shouldn’t have too much trouble (they’ve done harder
proofs before).
7. This proof will lead nicely into Theorem 12.12 which the students will also enter into their
notes.