Download Suggested Pacing for the Common Core Geometry Course

Suggested Pacing for the Common Core Geometry Course
Note: Textbook pages are for reference only. You will have to use additional resources since
the text does not follow the modules completely.
Unit 1: Angles and Constructions
Lesson
1
2/3
Title
Introduction to
Geometry
Constructions:
Copy Segment,
Equilateral 
Content
Define: Point, Line, Plane
Textbook Pages
Pg: 5-13
Define: Congruence, Segments, Betweenness, Midpoint,
Introduce Midpoint Formula
Introduce Distance as absolute value of difference of two
points and using the formula
Define: angle, types of angles:acute, right, obtuse, straight
,< bisector,
Introduce how to label an angle
Pg: 14-35
4
Constructions:
Copy an <,
Bisect an <,
Construct a 60 
angle
Pg: 36-44
5
Solve for Unknown
<’s
Define: Vertical <’s, Adjacent <’s, Complementary <’s,
Supplementary <’s,
Linear Pair, Straight <
Understand a full rotation is 360 
Pg: 46-54
6
Constructions:
 lines
 bisector,
45  angle
Symmetry: “  right
<’s
along  bisector
Define:  bisector, Right <’s, Symmetry
Theorems:  lines form right angles
Pg: 48,55,324
7/8
Point of
Concurrency:
Circumcenter - 
bisector
Incenter - < bisector
*Patty Paper*
Define: Concurrency, Circumcenter, Incenter
Pg: 324-331
9
10
Review
Test
Standards Addressed:
G-CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line, and distance around a circular arc.
G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying
an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point
not on the line.
G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Unit 2: Unknown Angles and Postulates of Equalities
Lesson
1
Title
Properties of Parallel
Lines
Content
Textbook Pages
Define: Parallel Lines, Transversal ,Theorem
Pg: 173-186
Theorems: Alternate Interior Angles are Congruent,
Alternate Exterior Angles are
Congruent,
Corresponding Angles are Congruent,
Same Side Interior angles areSupp.
2
3
Properties of Parallel
Lines
Angles in a Triangle
Construct parallel lines
Applications
Sum of Angles is 180 
Types of Triangles
Find missing angle/s of a triangle
Engage NY Mod 1 topic B
Lesson 7
Pg: 246-254
4
Angles in a Triangle
Exterior angle of a Triangle Theorem
Pg: 246-254
5
Write Unknown <
Proofs
“Informally”
Define: Hypothesis, Conclusion, Conditional
sentences
Deductive reasoning
Pg: 127-134
Postulates of Equality
Reflexive, symmetric, transitive, substitution,
addition, subtraction,
mult, div
Proofs using all definitions and postulates from this
unit
Pg: 136-140
6-8
9
Practice Proof Day
10
11
Review for test
Test
Pg: 144-159
Supplement with
worksheets
Standards Addressed:
G-CO.C.9
1
Prove1 theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
Prove and apply (in preparation for Regents Exams).
Why are TRANSFORMATIONS THE SPINE OF THE CORE?
Isometries& Rigid Motions in the plane preserve distances, angles, betweeness and
collinearity within transformed shapes. This leads to our new definition of congruence.
Two figures are CONGRUENT if and only if one can be obtained from the other by
one or a sequence of rigid motions.
The non-isometric transformation of dilation leads us to investigating similarity. This
definition is also revised to be viewed in the light of transformations.
Two plane figures are SIMILAR if and only if one can be obtained from the other by
one or a sequence of similarity transformations. (Similarity transformations included
reflection, rotation, translation and dilation.)
Unit 3:Transformations/Rigid Motions
Lesson
1
Topic
Review of
Transformations
Content
Image and Pre- image, Clockwise and Counter
clockwise, Symmetry,
Review def of: Rotations, Line Reflections,
Translations[Distance and < measure is
preserved],
Dilations[not  ], Center of rotation
Textbook Pages
Ch 9 Pg: 621
2/3
Line Reflections
Graphically and Non-graphically
Constructions:
Using constructions locate the line of
reflection.
Students understand that any point on a line
of reflection is equidistant from any pair of
pre-image and image points in a reflection.
Characterize points on a perpendicular
bisector.
Graphically and Non-graphically
Constructions
Pg: 623-629
Graphically and Non-graphically
Constructions and rotational symmetry
Pg: 651-657, 663-669
4
Translations
5
Rotations,
Reflections,
Symmetry
“Compositions”
Pg: 632-636
6
Rotations
Graphically and Non-graphically
Constructions
7
Point Reflections
Show reflection in origin as well as any point.
Discuss it’s a rotation of 180, point symmetry
8/9
Apply and Construct
Composition of
figures
10
Applications of  in
terms Of Rigid
Motion
Show and describe compositions of
transformations such as two line reflections,
translation and line reflection, etc. Write in
words only, no symbols.
Corr. Parts of   ’s are 
Must be able to identify corresponding parts
of  figures after a single transformation has
occurred
11
12
Review
Test
Pg: 639-346
Pg: 651-656
*See directions in Engage NY
modulePg:147-153
Text: Pg: 255-260
Pg: 296-299
Standards Addressed:
G-CO.A.2
Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those that do not (e.g., translation
versus horizontal stretch).
G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections
that carry it onto itself.
G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,
e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid
motions to decide if they are congruent.
G-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a
point not on the line.
Unit 4: Triangle Congruence
Lesson
1-5
Topic
Congruence of
triangles by
SSS,SAS,ASA,AAS,
HL
6
7
Showing Base
Angles of an
Isosceles Triangle
are congruent
Triangle proofs
8
9
10
Triangle proofs
Review
Test
Content
Manipulating physical forms of triangles
through rigid motions to determine whether
or not a pair of triangles is congruent.
Students must be able to write the series of
compositions of transformations from the
pre-image to the image to show triangles are
congruent by different methods.
Students should recognize method of
congruence by triangle markings and
determine missing part so triangles would be
congruent.
Formal proofs.
Proof should be done by construction as well
as a formal proof.
Textbook Pages
Pg:264-271
Pg: 275-282
Pg: 275-284
Practice day on writing proofs including
supplementary angles and CPCTC
Practice day on writing proofs
Ch 4 pg: 264-293
Pg. 285-291
Ch 4 pg: 264-293
Standards Addressed:
G-CO.B.7
G-CO.B.8
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
Unit 5: Quadrilaterals
Lesson
1
2,3
4-8
9
10
Topic
Properties of
Parallelograms
Practice proof day on
parallelograms
Properties of other
quadrilaterals
Review
Test
Content
Students should identify the 6 properties
of a parallelogram
Proofs and algebraic applications
Given parallelogram, write proofs
Prove quad is a parallelogram
Discuss properties of rectangle,
rhombus, square,trapezoid,kite
Textbook Pages
Pg:403-411
Supplement with old texts
Pg: 423-448
Standards Addressed:
G-CO.C.11 Prove2 theorems about parallelograms. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles
are parallelograms with congruent diagonals.
Unit 6: Segments in Triangles and Constructions
1
Special lines in triangles:
mid segment
2
Special lines in triangles:
centroid
3
Special lines in triangles:
orthocenter
Construct a square and
A regular hexagon
inscribed in a circle
4
5
Sum of Interior/Exterior
angles of a polygon
6
7
Review
Test
Construct the mid segment of a triangle
and discuss the mid-segment of a
triangle is parallel to the third side of the
triangle and half the length of the third
side of the triangle. Include midsegment
of a trapezoid
Construct the centroid as point of
concurrency of medians.
Discuss the ratios of the segments of the
median. Show coordinates of centroid is
the average of the three vertices of the
triangle.
Construct orthocenter as point of
concurrency of altitudes.
Using construction of copying segments
and perpendicular lines, construct a
square.
Using the length of the radius of a circle,
mark off 6 equal parts of circle to find
vertices of a hexagon
Using formula 180(n-2) find sum of the
measures of angles of polygons, each
angle, ext angle
Pg:491
Pg. 440
Pg: 334-335
Module pg. 156-165
Pg: 337
See handout from Math Open
Reference
Pg: 393-399
Standards Addressed:
G-CO.C.10
Prove2 theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a
triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Unit 7: Inequalities
Lesson
1
Topic
Basic inequality postulates
Inequalities involving sides and angles of
triangles
2
Inequalities involving exterior angle of
triangle
3
Triangle inequality involving sides
Triangle inequality proofs (optional)
4
5
Content
Introduce basic inequality
postulates.
Show smallest angle
opposite shortest side, etc
Show exterior angle is
greater than either nonadjacent interior angle
Sum of two sides is greater
than third side
Practice proofs
Textbook Pages
Pg: 344-350
Pg: 344-350
Pg: 364-368
Throughout chapter 5 in
text
Review
Test
Standards Addressed:
G-CO.C.10
Prove2 theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a
triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Unit 8a: Scale Drawings and Dilations
Lesson
1
Topic
Scale Drawings
2
Making scale drawings
using the ratio method
3
Constructing a line
parallel to a given line in
a triangle.
4
Dividing segments into n
equal parts
*End here for midterm
Content
Discuss: properties of a scale drawing:
corresp angles congruent,
Constant of proportionality - scale factor
Students should be able to construct
scale drawings of a polygon using any side
and copying angles.
Students should recognize scale factors
when r = 1, r>1 and 0<r<1
Recall definition of dilation. Construct
scale drawings given specific ratios: 1:2,
etc.
Using the construction of a parallel line in
a triangle, discuss ratio of the segments
formed. (Module refers to this as "side
splitter thm". Solve numericals involving
proportions.
Using a compass and a ruler, use parallel
lines to create segments of different
ratios.
Textbook Pages
Pg: 511-517
Pg: 518-521
Pg: 490-498
Math Open Reference handout
EngageNY module 2 pg.141
Unit 8b: Scale Drawings and Dilations continued
Lesson
1/2
Topic
Similar Polygons
3
Dilations as Transformations of
the Plane
4
How do dilations map
segments?
5
Properties Under
Transformations
6
Compositions of
Transformations including
Dilations
7
8
Review
Test
Content
Define similarity, ratio of similitude,
Ratio of perimeters, altitudes,
medians, angle bisectors
Given 2 points, a center and a scale
factor, draw diagrams illustrating
lengths inc/dec by scale factor
Given an angle, a center and a scale
factor, show angle measurement
remains the same. Remind students
def of rigid motion and discuss
previous transformations.
Using coordinates, students will dilate
segments given values of r.
Dilation of a line.
Discuss properties preserved under
transformations, isometry,practice
multiple transformations
Identify the similarity transformation
that maps preimage to image. Write as
composition of transformations in
words/symbols.
Textbook Pages
Pg: 461-475
Pg: 674-683
EngageNY module 2 pg.85
Pg: 674-683
EngageNY module 2 pg.99
Pg: 674-683
Pg: 651-689
EngageNY module 2 pg.128
Standards Addressed:
G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor:
a.
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a
line passing through the center unchanged.
b.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the
other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy
physical constraints or minimize cost; working with typographic grid systems based on ratios).★
Unit 9: Similar Triangles
Lesson
1
Topic
The angle-angle criterion for two triangles to
be similar.
Similarity and the Angle Bisector Theorem
Content
Discuss similarity
transformations as the
composition of basic rigid
motions and dilations, SAS,
SSS,AA
Textbook Pages
Pg: 469-477
Pg: 501-507
2
Similarity
Applications of similar polygons
Numerical applications of
similar triangles
Use proportional parts with
parallel lines
Pg: 478-487
3
Proving Triangles Similar
Pg: 478-487
4
Using similar triangles to show corresponding
sides are proportional
Using similar triangles to show cross products
are equal
Review
Test
Use definitions to prove
triangles similar
Extension of similar triangle
proofs.
Extension of similar triangle
proofs.
5
6
7
Pg: 478-487
Pg: 478-487
Standards Addressed:
G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if
they are similar; explain using similarity transformations the meaning of similarity for triangles as the
equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be
similar.
G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree
trunk or a human torso as a cylinder).★
Unit 10: Applying Similarity to Right Triangles
Lesson
1
Topic
Special relationships within right triangles dividing into two similar sub-triangles
Content
Proving three triangles are
similar
Mean proportional theorem:
Altitude is mean proportional
between the segments on
the hyp
Mean prop thm: Leg is mean
prop.
Textbook Pages
Pg: 501-507
2
Special relationships within right triangles dividing into two similar sub-triangles
3
Multiplying and dividing expressions with
radicals
Simplify, multiply and divide
radical expressions
Rationalizing denominators
Honors: Using conjugates
P19-20
Supplement with other
resources
4
Adding and Subtracting radicals
Pythagorean Thm
Use distributive property to
illustrate adding and
subtracting radicals
Applications finding
perimeters of polygons,
shaded areas
Supplement with other
resources
30-60-90 and 45-45-90
triangles
Pg: 558-564
5
Special Right Triangles
P: 501-507
Pg: 546-553
6
7
Review
Test
Standards Addressed:
G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the
other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Unit 11: Trigonometry
Lesson
1
*
Topic
Trig Ratios: Sine, Cosine, Tangent
2
Trig Ratios: Secant, Cosecant and Cotangent
*honors
Cofunctions
3
Applications using sine and cosine
4
Applications using tangent
5
Trigonometry and the Pythagorean Theorem
6
7
Review
Test
Content
Find trig ratios using right
triangles
Use trig ratios to find angle
measures in right triangles
Introduce reciprocal trig
functions
Introduce relationship
between complementary
angles and ratios
Solve problems involving
angles of elevation and
depression.
Solve problems involving
angles of elevation and
depression.
Given one ratio, use
pythagorean theorem to be
able to find remaining trig
ratios.
Introduce pythagorean
identity
sin2x + cos2x = 1
Introduce quotient ratio :
tan x = sinx /cosx
Textbook Pages
Pg.568-577
Pg. 578
Engage NY Module 2
Pg: 407-410
Pg: 580-586
Pg: 580-586
EngageNY Module 2
Pg:437-452
Unit 11: Trigonometry continued
Lesson
1
2
Topic
Area of a triangle
Law of Sines
3
Law of Cosines
4
Applications of law of sines and cosines
5
6
Review
Test
Content
Show area = 1/2 absinC
Find missing side of acute
triangle
Find missing side of acute
triangle
Solve triangle problems
finding sides
Textbook Pages
See module
Pg. 588-599
Pg. 588-599
Pg. 588-599
Standards Addressed:
G-SRT.C.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
leading to definitions of trigonometric ratios for acute angles.
G-SRT.C.7
Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
Unit 12: Area
Lesson
1
Topic
Areas of Triangles, Quadrilaterals
2
Applications of Areas of Similar Figures
3
Circumference and arc length
4
5
6
7
8
9
Area of Circles and Sectors
Areas of Regular Polygons Involving apothem
Areas of Composite Figures
Cross Sections
Review
Test
Content
Find area of: triangle,
parallelogram, rhombus,
kites, trapezoid
Comparing the ratio of
areas to ratio of sides of
similar polygons
Circumference and arc
length, radian measure
Include shaded areas
Textbook Pages
Pg: 779-795
Pg. 818-822
Pg. 699-713
Pg: 798-805
Pg:807-813
Pg. 807-813
Pg. 840
Standards Addressed:
G-GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume
of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit
arguments.
Unit 13: Surface Area and Volume
Lesson
1
Topic
Three Dimensional Space
2
Surface Areas
3
Surface Areas
4
Volume of Prism and Cylinder
5
Volume of Pyramid and Cone
6
Surface Area and Volume of a Sphere
7/8
Volume of Composite Figures
9
10
Review
Test
Content
Introduce solid figures:
Prism, cylinder, pyramid
and cone
Show cross-sections
formed from intersection
of plane and solid
Find lateral area and
surface area of prisms and
cylinders
Find lateral area and
surface area of pyramids
and cones
Find volume of prism and
cylinder. Scaling principle
for volumes. Cavalieri's
Principal
Textbook Pages
Pg.839-843
Find volume of pyramid
and cone
Find surface area and
volume of sphere
Find volume of composite
3D figures
Pg. 873-878
Pg. 846-852
Pg. 854-861
Pg. 863-870
Pg. 880-886
See Exam Gen and NYS
Regents
Standards Addressed:
G-GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume
of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit
arguments.,
G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems.
G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify
three-dimensional objects generated by rotations of two-dimensional objects.
G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree
trunk or a human torso as a cylinder).
G-MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square
mile, BTUs per cubic foot).
G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy
physical constraints or minimize cost; working with typographic grid systems based on ratios).
Unit 14: Coordinate Geometry
1
Slope as Rate of Change
Writing the equation of a line given
Slope and a point, or two points
2
Perpendicular lines and distance
3-5
Coordinate Geometry Proofs
Define slope in
coordinate plane as rate
of change.
Applications using slope
Discuss relationship
between slopes of
parallel and
perpendicular lines
Write equation using
point slope form and
slope intercept form
Discuss all points on
perpendicular bisector of
a line are equidistant
from the endpoints
Write the equation of
the perpendicular
bisector
Prove or disprove a
quadrilateral is a
parallelogram, rectangle,
rhombus, square,
trapezoid using distance
and slope.
Include literal
coordinates
Pg. 188-195
Pg. 198-204
Pg.215-221
Pg. 419,427,436,444
6
Perimeter and Area of Polygons
7
Dividing Segments Proportionately
8
9
Review
Test
Using Coordinate Plane,
find perimeter and area
of triangles and
polygonal regions.
Partitioning segments on
coordinate plane into
ratios other than 1:1
Pg. 56-63
Supplement with
worksheets
Module pg. 145
Standards Addressed:
2
G-GPE.B.4
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove
that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that
the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
G-GPE.B.5
Prove 2 the slope criteria for parallel and perpendicular lines and use them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given
point).
G-GPE.B.6
Find the point on a directed line segment between two given points that partitions the segment in a
given ratio.
G-GPE.B.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using
the distance formula.★
2F
Prove and apply (in preparation for Regents Exams).
Unit 15: Circles - Angles
Lesson
1
Title
Intro to Circles
Measuring angles and arcs
Inscribed Angles
2
Arcs and Chords
3
Inscribed and Circumscribed circles of a
triangle
4
5-7
Tangents
Secants, Tangents, Chords, Angles
8
Practice day on all circle applications
9
10
Review
Test
Content
Define circle, radius,
diameter, chord, arc,
concentric circles
Show all circles are similar
Discuss major/minor arc,
semi circle, central angles.
Thales Thm: Opposite
angles of a quad inscribed
in a circle are
supplementary
Diameter perpendicular to
chord
Congruent chords have
congruent arcs, etc.
Construct a circle inscribed
in a triangle
Construct a triangle
circumscribed about a
circle
Tangents drawn to a circle
Measuring angles and arcs
formed by sec, tan, chords
Putting it all together into
multi-step circle questions
Textbook Pages
Pg. 697-705
Pg. 706-714
Pg. 723-730
Pg. 715-722
Pg. 740
Pg. 732-739
Pg. 741-749
See module for examples
Standards Addressed:
3
G-C.A.2
Identify and describe relationships among inscribed angles, radii, and chords. Include3 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.A.3
Construct the inscribed and circumscribed circles of a triangle, and prove4 properties of angles for a
quadrilateral inscribed in a circle.
G-C.B.5
Derive 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.
Include angles formed by secants (in preparation for Regents Exams).
Unit 16: Circles - Segments
Lesson
1
Title
Segments of chords in a circle
2
Tan-sec and 2 sec segments
3
Writing the Equation of a Circle
4
Recognizing the Equation of a Circle
*
Equations of Tangents to Circles (honors)
5/6
7
8
9
Circle Proofs
Dilating circles by construction
(**optional topic)
Content
Finding length of chords in
a circle
Finding the length of
tan/sec segments
Write equation given
center, radius
Completing the square
Writing equation of tan line
given equation of circle,
slope of tan line
Using circle angles and
segments to prove
triangles congruent and
similar.
Constructing circles of scale
factors greater than one
and less than one, with
center of dilation inside or
outside the circle.
Writing the equation of a
circle given a scale factor.
Textbook Pages
Pg. 750-756
Pg. 750-756
Pg. 757-762
Pg. 757-762
Module pg. 227-236
Module pg. 237
Use ExamGen for examples.
Module 2 Lesson 8 pg. 120
**See link below from
Manhassetschools for a
sample lesson
Review
Test
Standards Addressed:
G-C.A.1
Prove4 that all circles are similar.
G-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle given by an equation.
G-GPE.B.4
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove
that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that
the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
End of curriculum! 151 days of instruction including review and exams
Here is a nice website that links the standards to all topics in the CC Geometry curriculum:
http://www.mathsisfun.com/links/core-high-school-geometry.html
GEO H – Dilating Circles by Construction:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CCsQFjACahUKEwiTwcCItaHHAhXL
aT4KHbTiDJ4&url=http%3A%2F%2Fmanhassetschools.org%2Fsite%2Fhandlers%2Ffiledownload.ashx%3Fmoduleinstanceid%3D3700
%26dataid%3D7804%26FileName%3DAim%25208%252010H.pdf&ei=DR7KVdOGGcvTQG0xbPwCQ&usg=AFQjCNELM6tjMrOkex704D4spPjBxiIRRA&bvm=bv.99804247,d.cWw
4
Prove and apply (in preparation for Regents Exams).