Type of Class: All levels of high school Geometry

Related VA SOL: G.8

Time Frame: 90-minute block period

Objectives:

·        Students will know different ways to prove that a particular quadrilateral is a parallelogram.

·        Students will know different ways to prove that a particular parallelogram is a rectangle.

·        Students will know different ways to prove that a particular parallelogram is a rhombus.

Materials:

·        Geometer’s Sketchpad 4.0

·        Worksheet

Procedures:

1.      Students are split up in pairs or groups of three. They are assigned one of the theorems listed on worksheet #2.

2.      Students will prove their specific theorem in a two-column proof. They can use Geometer’s Sketchpad and any other notes to help them. By this time, students should be able to reason deductively.

3.      With their theorem, students will create an algebra problem similar to the ones they have done in the past.

Show that the quadrilateral is a parallelogram. Then find each length and measure.[1]

a.       mÐDAB

b.      BC

c.       DC

4.      With their theorem, students will create a coordinate problem.

Prove that the diagonals of the parallelogram ABCD are perpendicular.

5.      Students will present their two-column proof in front of their peers.

Assessment:
Teacher will collect the worksheets and create a new worksheet with the students’ algebra and coordinate problems combined. They should be able to work through these problems, especially after learning the proofs for each of them. For the test, the teacher should add at least three proofs for students to prove.

Suggestions/Comments (if applicable):
Make sure that students’ algebra and coordinate problems are valid and useful. Students in the lower level Geometry might have problems creating math problems. Make sure you help them as much as possible.