Type of Class: Honors Geometry

Related VA SOL: G.10

Time Frame: 90-minute block period

Objectives:

·        Students will identify types of arcs and angles in a circle.

·        Students will compare central and inscribed angles.

·        Students will be able to find the measures of arcs and angles.

·        Students will be familiar with the inscribed angle theorems.

Materials:

·        Geometer’s Sketchpad 4.0

·        circleA.gsp

·        circleF.gsp

·        circleE.gsp

·        circleD.gsp

·        Worksheet

Procedures:

1.      Students should work in pairs for this assignment.

2.      Introduce definitions of central angle, inscribed angle and chord by Concept Attainment.

3.      Explore Worksheet #1 Part A that compares central and inscribed angles.

4.      Review Worksheet #1 Part A, especially the extra credit part. Discuss tangent and point of tangency of a circle.

Tangent Theorem: A line, a ray, or a segment is tangent to a circle if and only if it is in the same plane as the circle and is perpendicular to a radius of the circle at the point of intersection.[1]

5.      Introduce definitions of arc, minor arc, major arc, and semicircle by Concept Attainment.

6.      Explore Worksheet #1 Part B.

Arc Addition Postulate: In a circle, the measure of the arc formed by two arcs that have exactly one point in common is the sum of the measures of the two arcs.[2]

7.      Introduce congruent arcs by showing examples from earlier work or giving the formal definition.

8.      Explore Worksheet #1 Part C.

Inscribed Angle Theorems: [3]

1.      The measure of an inscribed angle is equal to half the measure of the intercepted arc.

2.      In a circle or in congruent circles, inscribed angles that intercept the same arc or congruent arcs are congruent.

3.      The measure of an angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.

Assessment:
When students have finished the worksheet, the teacher should have students form in groups of four to six. Students will share their observations and together, create a well-written conjecture for each topic and present it to the class. The teacher should create tests and quizzes based on what they discovered in the lab.

Suggestions/Comments (if applicable):
The lesson can be used for other levels in Geometry. However, it may take two days to finish it.