Download GEOMETRY E10

GEOMETRY
(SECONDARY)
ESSENTIAL UNIT (E10)
(Circles)
(July 2013)
Unit Statement: The properties of circles, including their tangents and secants, arcs and
their angles, segments and sectors, are identified and employed to solve problems. The
equation of the circle in coordinate geometry is also presented and employed.
Essential Outcomes: (must be assessed for mastery)
Problem solving and higher order thinking components are essential for ‘A’ level
mastery. Each outcome can contain problem solving and higher order thinking
components (as found in suggested text).
1. The Student Will identify tangents, secants, and chords and use properties of
tangents to solve problems (12.1 pp 792 - 800).
2. TSW apply properties of arcs and chords to solve problems (12.2 pp.802 - 809).
3. TSW find arc lengths and areas of sectors (12.3 pp. 810 - 815).
4. TSW find the measures of inscribed angles and use their properties to solve
problems (12.4 pp. 820 - 827).
5. TSW find the measures of angles formed by lines that intersect circles and use the
angle measures to solve problems (12.5 pp. 830 - 837).
6. TSW find the lengths of segments formed by lines that intersect circles and use the
lengths to solve problems (12.6 pp. 840 - 846).
7. TSW write equations and graph circles in the coordinate plane and use the
equations to solve problems (12.7 pp. 847 - 853).
Introduced and Practiced Outcomes: (taught not assessed)
1. The Student Will use proportions to convert angle measures from degrees to
radians (12.3 pp. 816-817).
Key Terms and Concepts:
adjacent arcs
chord
congruent circles
interior of circle
secant
semicircle
arc
common tangent
exterior of circle
major arc
secant segment
subtend
arc length
central angle
concentric circles
congruent arcs
inscribed angle
intercepted arc
minor arc
point of tangency
sector of circle segment of circle
tangent of circle
tangent segment
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QSI GEOMETRY SEC E10
Copyright © 1988-2013
Suggested Assessment Tools and Strategies:
Attached Rubric or teacher generated rubric that assesses ALL essential outcomes
(TSWs).
Suggested Resources:
Holt McDougal Geometry, Chapter 12, Sections 1 - 7.
Holt McDougal Geometry, Problem Solving Workbook
Holt McDougal Geometry, Practice Worksheets
Holt McDougal Geometry, Reading Strategies
Holt McDougal Geometry, Reteach Worksheets
Holt McDougal Geometry, Challenge Worksheets
Holt McDougal Geometry, Assessment Resources
Technology Links:
Holt McDougal Geometry, Online Edition, 6-year subscription
Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM
Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM
Holt McDougal Geometry, Teacher One-Stop DVD
On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM
On Core Mathematics High School Activity Generator CD-ROM
Follett Destiny WebPath Express (found on school’s automated library system)
Tenmarks www.tenmarks.com/
Khan Academy https://www.khanacademy.org/
PhET Simulations http://phet.colorado.edu/en/simulations/category/math
EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………..
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QSI GEOMETRY SEC E10
Copyright © 1988-2013
UNIT EVALUATION RUBRIC


Geometry
Essential Unit 10 (E10)
To receive a ‘B’, the student must show ‘B’ level mastery on all seven TSW’s.
To receive an ‘A’, the student must show ‘A’ level mastery in at least 4 of the 7
available TSW’s and ‘B’ level mastery on all of the remaining TSW’s.
‘A’ LEVEL
‘B’ LEVEL
1- identify tangents,
secants, and chords
and use properties of
tangents to solve
problems.
The student is able to state if it
is possible to draw tangents to
circles given various
information about the circles.
The student can identify
tangents, secants, and
chords and use properties
of tangents to solve
problems.
2- apply properties of arcs
and chords to solve
problems.
The student is able to
construct a circle through
three noncollinear points.
The student is able to
apply properties of arcs
and chords to solve
problems.
3- find arc lengths and
areas of sectors.
The student can find arc
lengths of circles with
different radii which would
yield equal sector areas.
The student can find arc
lengths and areas of
sectors.
4- find the measures of
inscribed angles and
use their properties to
solve problems.
The student is able to use
angle measures of inscribed
polygons to justify that the
sum of the interior angles of a
triangle is 180.
The student can find the
measures of inscribed
angles and use their
properties to solve
problems.
5- find the measures of
angles formed by lines
that intersect circles
and use the angle
measures to solve
problems.
The student can design a
multi-step proof using angles
formed by lines that intersect
circles.
The student is able to
find the measures of
angles formed by lines
that intersect circles and
use the angle measures to
solve problems.
6. find the lengths of
segments formed by
lines that intersect
circles and use the
lengths to solve
problems.
The student is able to extend
the Chord-Chord Product
Theorem to prove the
Pythagorean Theorem.
The student can find the
lengths of segments
formed by lines that
intersect circles and use
the lengths to solve
problems.
7. write equations and
graph circles in the
coordinate plane and
use the equations to
solve problems.
The student can solve
complex, multi-step story
problems involving circular
areas on a map.
The student can write
equations and graph
circles in the coordinate
plane and use the
equations to solve
problems.
TSW
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QSI GEOMETRY SEC E10
Copyright © 1988-2013
Notes