Type of Class: Honors Geometry

Related VA SOL: G.10

Time Frame: 90-minute block period

Objectives:

·        Students will investigate the lengths of chords, tangents and secants and their relationships.

·        Students will be able to find the area of a sector.

·        Students will be able to find the length of an arc.

·        Students will investigate applications of architecture, art, and construction using the properties of chords, tangents, and secants.

Materials:

·        Geometer’s Sketchpad 4.0

·        lengthseg.gsp

·        Large pizza with 14 inch diameter

·        Small pizza with 10 inch diameter

·        Worksheet

Procedures:

1.      Explore the segment lengths on worksheet #3.

Length of Chords and Secants: [1] 

         Lengths of Tangents and Secants: [2]

   

2.      Give algebraic examples using the theorems above. For instance:

Text Box: Let QT = 15, PT = 12.5, RT = 2x + 6 and TS = 3x + 1. Find RT and ST.

 

 

 

3.      Teacher will bring in two whole pizzas. The small pizza will have a diameter of 10 inches and the large pizza will have a diameter of 14 inches. Students will find the area of a sector. (Hint: Area of slice = 1/8 * area of pizza)

 

Area of a Sector:[3] If x represents the measure of the arc of a sector and r is the radius of the circle, then

Area of the sector = x/360 * π r 2

4.      Give examples using the formula of the area of a sector. For instance:

 

Text Box: The area of the red sector is 8 π cm2 and BC = 6 cm. Find mÐABC.

 

 

5.      Students will find the length of arc.

 

Length of an Arc: If x represents the measure of an arc and r is the radius of the circle, then

Length of the arc = x/360 * 2 π r. [4]

6.      Give examples using the formula of the length of an arc. For instance:

Find the length of the minor arc EF. 

7.      Students will work on the last two real world application problems on the worksheet.

Assessment:
Students should be tested on the conjectures or theorems that they made during the lab and pizza activities.  For further assessment, let students explore and find the relationship between the four theorems and prove why they are true. Create more hands-on activities on finding the area of a sector or an arc length.

Suggestions/Comments (if applicable):
The lesson can be used in other levels of Geometry. Give more algebra problems like the one above so that students will have more practice. Instead of a pizza activity, you can have three or four students bake cakes of different sizes.

[1] Aichele, D.B., Hopfensperger, P.W., Leiva, M.A., Mason, M.M., Murphy, S.J., Schell, V.J., Vheru, M.C. (1998). Geometry: Exploration and application. Evanston, IL:  McDougal Littell, 561.

[2] Aichele, D.B., Hopfensperger, P.W., Leiva, M.A., Mason, M.M., Murphy, S.J., Schell, V.J., Vheru, M.C. (1998). Geometry: Exploration and application. Evanston, IL:  McDougal Littell, 574.

[3] Aichele, D.B., Hopfensperger, P.W., Leiva, M.A., Mason, M.M., Murphy, S.J., Schell, V.J., Vheru, M.C. (1998). Geometry: Exploration and application. Evanston, IL:  McDougal Littell, 574.

[4] Aichele, D.B., Hopfensperger, P.W., Leiva, M.A., Mason, M.M., Murphy, S.J., Schell, V.J., Vheru, M.C. (1998). Geometry: Exploration and application. Evanston, IL:  McDougal Littell, 580.