Exploring Bisectors, Medians, and Altitudes of a Triangle with Cabri Jr

Vickie Baier

Lesson Plan

Exploring Bisectors, Medians, and Altitudes of a Triangle with Cabri Jr.

NCTM Expectations:

Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them

Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

Illinois Learning Expectations:

GOAL 9: A. Demonstrate and apply geometric concepts involving points, lines, planes and space.

GOAL 9: B. Identify, describe, classify and compare relationships using points, lines, planes and solids.

GOAL 9: C. Construct convincing arguments and proofs to solve problems.

Lesson Objectives:

· Use properties of perpendicular bisectors of a triangle

· Use properties of angle bisectors of a triangle

· Use properties of medians of a triangle

· Use properties of altitudes of a triangle

Materials Needed:

· Textbook

· Power Point with warm-up and review

· Worksheets

· TI graphing calculators with Cabri Jr.

Class Breakdown:

1. Warm up and previous homework(20 minutes)

2. Discuss perpendicular bisectors, angle bisectors, medians, and altitudes of triangles using PowerPoint. This is a quick review of previous covered ideas.(10 minutes)

3. Divide into four groups using the worksheets and calculators to discover ideas about perpendicular bisectors, angle bisectors, medians, and altitudes of triangles. The worksheets (using parts from TI) will have numbers on them for the next segment. They will be doing part 1 on the worksheets. (30 minutes)

4. Switch groups to so there are four people in a group (one from each of the above groups). Each student will link their calculators so all students will have each activity. They will then each explain what they did and learned in part 1. Then in their group they will do part 2 on the worksheets. (30 minutes)

5. If time allows wrap it up as a class. Otherwise we will wrap it up the next day at the beginning.

6. Assign homework

Warm Up

Using a constant rate, a lumberjack cuts a log into 4 pieces in 12 minutes. At the same constant rate, how long will it take the same lumberjack to cut a similar log into 8 pieces?

Solution: It takes 3 cuts to get 4 pieces, so each cut takes (12/3)=4 minutes.

It will take 7 cuts to get 8 pieces, so 7cuts x 4min/cut = 28 minutes total.

Final Answer = 28 minute

Part 1: Median Name ______

A median of a triangle is a segment connecting a vertex to the midpoint of the opposite side.

Part 2: Summarize

On a separate piece of paper, organize your results and findings about the centroid, circumcenter, orthocenter and incenter of a triangle. Compare the properties of the different centers. How they are similar, how are they different, and how are they related.

Part 1: Angle Bisectors Name______

An angle bisector is the set of points equidistant from the sides of the angle.

Part 2: Summarize

Part 1: Altitude Name______

An altitude of a triangle is a segment from a vertex perpendicular to the opposite side or an extension an extension of the opposite side of the triangle.

Part 2: Summarize

Part 1: Perpendicular Bisector Name______

A perpendicular bisector of a segment is a line that is perpendicular to the segment at its midpoint.

Part 2: Summarize