Download Geometry Curriculum The length of part of a circle`s circumference

Geometry Curriculum
Paterson Charter School for Science and Technology
2014-2015
Unit 3 Summary: Circles
Essential Questions
Big Ideas
The length of part of a circle’s circumference can be found
by relating it to a central angle in the circle.
The area of a circle can be found when the circle’s radius
is known.
The area of parts of a circle formed by radii and an arc can
be found when the circle’s radius and the arc measures
are known.
Information about congruent parts of a circle (or congruent
circles) can be used to find information about other parts of
the circle (or circles).
Angles formed by intersecting lines have a special
relationship to the arcs the intersecting lines intercept.
Geometry Curriculum
Unit 4:Circles
Unit 3 Summary: Circles
Learning Outcomes (CCSS)
G.C.1 Prove that all circles are similar.
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.
G.C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
G.C.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian
measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Local Standards (LS) #24-25 are taught in this unit.
51. Prove that all circles are similar.
52. Find the circumference, measure of central angles and arcs of a circle.
53.
54.
55.
56.
57.
58.
59.
Use congruent chords, arcs, central angles and perpendicular bisectors to chords.
Identify and describe relationships among inscribed angles, radii and chords.
Construct the inscribed and circumscribed circles of a triangle.
Prove properties of angles for a quadrilateral inscribed in a circle.
Derive using similarity that the fact that the length of the arc intercepted by an angle is proportional to the radius.
Define the radian measure of the angle as the constant of proportionality.
Derive the formula for area of sector.
Geometry Curriculum
Unit 4: Circles
Unit 3 Summary: Circles
Prior Knowledge Expected
Basic parts of circle.
Assessment Summary
1. Mid Unit Assessment (LS#51-54)
2. End-of-Unit Assessment (LS #55-59)
(Scope and Sequence on the next page)
Geometry Curriculum
Unit 4:Circles
Unit 1 Scope and Sequence: Number System Fluency
Periods*
CCSS
LS
Student Friendly Language
Resources
Textbook
Pearson 10-6
Links
1
G.C.1
S51
Prove that all circles are similar.
Other
Find the circumference, measure of central angles and arcs of
1
G.C.1
S52
Assessment
Skill Check 51
Textbook
Pearson 10-6
Links
a circle.
Other
Assessment
Skill Check 52
Textbook
1
G.C.1
S53
Use congruent chords, arcs, central angles and
perpendicular bisectors to chords.
Links
Other
1
G.C.2
S55
Identify and describe relationships among inscribed angles,
radii and chords.
Assessment
Skill Check 53
Textbook
Pearson 10-6, Concept Byte 106, 12-2, 12-3
Links
Geometry Curriculum
Unit 4: Circles
Other
1
G.C.3
S56
Construct the inscribed and circumscribed circles of a
triangle.
Assessment
Skill Check 55
Textbook
Pearson 5-3
Links
Other
1
G.C.3
S57
Prove properties of angles for a quadrilateral inscribed in a
circle.
Assessment
Skill Check 56
Textbook
Pearson 12-3
Links
Other
Assessment
Textbook
Skill Check 57
Pearson 10-6, 10-7
Links
1
G.C.5
S58
Define the radian measure of the angle as the constant of
proportionality.
Other
1
G.C.5
S59
Derive the formula for area of sector.
Assessment
Skill Check 58
Textbook
Pearson 10-6, 10-7
Links
Other
Geometry Curriculum
Unit 4:Circles
Assessment
Geometry Curriculum
Skill Check 59
Unit 4: Circles