Type of Class: Honors Geometry

Related VA SOL: G.10

Time Frame: 90-minute block period

Objectives:

·        Student will investigate a real world application dealing with secants.

·        Students will know the relationship between the measure of an angle and its minor and major arc.

·        Students will be able to calculate the measurement of an angle by two intersecting chords.

·        Students will know relationships between a diameter and a chord when they are perpendicular to each other.

Materials:

·        Geometer’s Sketchpad

·        Secants.gsp

·        Chords.gsp

·       Worksheet

Procedures:

1.      Students will work in pairs.

2.      On worksheet #2, students will read and solve the first word problem. This is an introduction to secants.

Angles formed by tangents and secants: the measure of an angle formed by the intersection of two tangents, two secants, or a secant and a tangent, at a point outside a circle, is half the difference of the measures of the intercepted arcs.

3.      Give an example of finding the measure of an angle, when given the measurements of a minor arc and major arc. Also, give an example where the sum of the minor arc and major arc is a semicircle.

Arcs formed by intersecting chords: the measure of an angle formed by two chords is equal to half the sum of the measures of the intercepted arcs.

4.      Give an example of the students’ construction using algebra:

Find the value of z and the measure of each labeled arc.

Chord Bisector Theorems

a.       The perpendicular bisector of a chord passes through the center of the circle.

b.      A diameter that is perpendicular to a chord bisects the chord and its corresponding arc.

 

5.      Give an example of what students explored using algebra:

BD ^ AC. Find mAB and mBC

Text Box: mBC = 2x + 1

 

Text Box: mAB = 3x - 35

                                         

Assessment:

When the students have finished their exploration, the teacher should form the class into groups of four to six. Students will share their observations and create a well-written conjecture for each topic together and present it to the class. The teacher should create tests and quizzes based on what the students discovered in the lab and the example algebra problems that the teacher presented.

 

Suggestions/Comments (if applicable):

The lesson can be used in other levels of Geometry.