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Geometry – Circle Unit
Erica Reese, Math Instructor
Emma Willard School
Troy, NY

Name: _________________________                          Due Date: ____________

Goals:

Day 1:  Identify parts of circles. Recognize major arcs, minor arcs, semicircles, and central angles.  Find measures of arcs and central angles.

Day 2:   Recognize and use relationships among arcs, chords, and diameters.

Day 3:   Recognize and find measures of inscribed angles.  Apply properties of inscribed figures.

Day 4:   Recognize tangents and use properties of tangents.

Day 5:   Find the measures of angles formed by intersecting secant and tangents in relation to intercepted arcs.

Day 6:   Use properties of chords, secants, and tangents to solve segment measure problems.

C Layer – no more than 78 points

_______        Day 1:  Choose Three (4 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 449, 450:  14-24, 29-36; pg. 456: 19-28, 34, 37-42 **

c.                  Draw five concentric circles with radii of 1”, 2”, 3”, 4”, and 5”.  Measure the circumference of each circle using a string and a ruler.  Calculate the ratio of circumference to diameter for each of the 5 circles.  See your teacher for the required materials.  Discuss your results with a partner.

d.                  Complete pg. 450: 40 (Draw a picture)

e.                  Draw a Venn diagram that illustrates the relationship among congruent, similar, and concentric circles.

_______        Day 2:  Choose Three (4 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 462, 463:  13-15, 17-27, 32-36 **

c.                  Work with a partner to complete pg. 461: 4.  See your teacher for the required materials.

d.                  Work with a partner to complete pg. 464: 45.  See your teacher for the required materials.

_______        Day 3:  Choose Three (4 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 470, 471: 17-45 **

c.                  Complete pg. 472: 56 (Draw a picture)

d.                  Suppose ABCD is a trapezoid that has its vertices on circle P, with AB || CD.  Write a 2-column proof to show that ABCD is an isosceles trapezoid.

_______        Day 4:  Choose Three (5 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 479, 480: 17-30 (Draw the figure on your paper), 31-36, 38, 39 **

c.                  Complete pg. 478: 5.  See your teacher for the required materials.

d.                  Complete Practice 9-5.

e.                  Work with a partner to complete pg. 481: 50 (Draw the figure on your paper)

_______        Day 5:  Choose Three (5 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 487, 488: 14-32, 37-43 **

c.                  Complete pg. 489: 49 (Draw a picture)

d.                  Complete pg. 490: 50 (Draw a picture)

_______        Day 6:  Choose Three (4 pts/each)                      ** means required

a.                  Listen to the lecture and take notes.

b.                  Complete pg. 495, 496: 14-26, 29, 30 **

c.                  Draw one figure for all three theorems discussed in this lesson.  Write an equation for each theorem relating the measures of the segments in your figure.  Check each equation by measuring the segments involved in the equations and finding the products.  Discuss your results with a partner.

d.                  Complete pg. 496: 36.

B Layer – no more than 10 points

_______        1.         Complete “The Circumference/Diameter Ratio” using The Geometer’s Sketchpad.

2.                  Complete “The Cycloid” using The Geometer’s Sketchpad.

3.                  Work with a partner to complete “Tilted Circles,” a Cooperative Learning Project on pg. 509.  See your teacher for the required materials.  Prepare a presentation on your work.

A Layer – no more than 10 points

_______        1.         Before it was discovered that Earth revolved around the Sun, it was believed that the sun and all the planets revolved around Earth in perfect circular orbits.  This model was known as the Ptolemaic system.  Read about this model and draw a diagram of the solar system according to Ptolemy.

2.         Go to www.phschool.com/math/awsm/geometry/geo.html and complete two out of the three Super Lessons that are listed under Chapter 8:

a.         Circles, Circumference, and Area

b.         Angles, Arcs, and Chords

c.         The Inscribed Angle Theorem

4.                  Cutting Down on Waste.  You wish to cut five discs out of a square piece of tin.  The discs can be any size.  If you want to use as much tin as possible, where should the discs be located in the square, and what should be their radii?  Explain how you have come to your conclusion.  Then, demonstrate your results by cutting comparable disks out of a square piece of cardboard or wood.

Day 7:  Chapter 9 Review

Day 8:  Chapter 9 Test