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South Henry School Corporation ● Tri High School ● Straughn, Indiana
Curriculum Map
Course Title: Geometry
Quarter: 1
Academic Year: 2013-2014
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
Standards
Chapter 1 Tools of
Geometry
1.1 Patterns and Inductive
Reasoning
1.2 Points, Lines and
Planes
1.3 Segments, Rays,
Parallel Lines and Planes
1.4 Measuring Segments
and Angles
1.5 Basic Constructions
1.6 The Coordinate Plane
1.7 Perimeter,
Circumference, and Area
State Standards
G.1.1
G.1.2
G.1.3
G.1.4
G.1.5
G.1.7
G.2.4
G.5.1
G.5.3
G.5.4
G.7.1
Common Core
Chapter 2 Reasoning
Standards
and Proof
CC.9-12. G.CO.1
2.1 Conditional Statements CC.9-12.G.CO.2 CC.912.G.CO.5
2.2 Biconditionals and
CC.9-12.G.CO.9
Definitions
CC.9-12.G.CO.10
2.3 Deductive Reasoning
CC.9-12.G.CO.11
2.4 Reasoning in Algebra
CC.9-12.G.CO.12
2.5 Proving Angles
CC.9-12.A.SSE.1 CC.9Congruent
12.A.CED.4
Content
Apply basic facts
about points, lines,
planes, segments,
and angles.
Measuring and
constructing
segments and
angles.
Using formulas to
find distance and the
coordinates of a
midpoint.
Skills







Identifying
reflections, rotations,
and translations.
Inductive and
deductive reasoning.
Using conditional
statements and
biconditional
statements.
Justifying solutions





Identify, name, and draw points,
lines, segments, rays, and
planes.
Apply basic facts about points,
lines, and planes
Use length and midpoint of a
segment.
Construct midpoints and
congruent segments.
Name and classify angles.
Measure and construct angles and
angle bisectors.
Identify adjacent, vertical,
complementary, and supplementary
angles.
Find measures of pairs of angles.
Apply formulas for perimeter, area,
and circumference.
Develop and apply the formula for
midpoint.
Use the Distance Formula and the
Pythagorean Theorem to find the
distance between two points.
Identify reflections, rotations, and
translations.
Assessment
Textbook
assignments
Worksheet
assignments
Resources
Textbook Prentice
Hall Geometry 2004
Edition
Smart Response
Technology
Quizzes
YouTube Videos
Tests
Oral Responses
Observations
Ipad Apps for
Geometry
Elmo and large
screen TV
presentations
Teacher generated
worksheets
PowerPoint
Presentations
South Henry School Corporation ● Tri High School ● Straughn, Indiana
Curriculum Map
Course Title: Geometry
Quarter: 1
Academic Year: 2013-2014
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
Chapter 3 Parallel and
Perpendicular Lines
(1st half of Chapter)
3.1 Properties of Parallel
Lines
3.2 Proving Lines Parallel
3.3 Parallel Lines and the
Triangle Angle-Sum
Theorem
3.4 The Polygon AngleSum Theorems
3.5 Lines in the Coordinate
Plane
Standards
CC.9-12.G.GPE.7
CC.9-12.G.SRT.4
Content
to algebraic
equations.
Skills


Standards for
Mathematical Practice
SMP1
SMP2
SMP3
SMP4
SMP5
SMP6
SMP7
SMP8
Writing two-column,
flowchart, and
paragraph proofs.
Parallel and
perpendicular lines.
Angles formed by
parallel lines and a
transversal











Graph transformations in the
coordinate plane.
Use inductive reasoning to identify
patterns and make conjectures.
Find counterexamples to disprove
conjectures.
Identify, write, and analyze the truth
value of conditional statements.
Write the inverse, converse, and
contrapositive of a conditional
statement.
Apply the Law of Detachment and
the Law of Syllogism in logical
reasoning.
Write and analyze biconditional
statements.
Review properties of equality and
use them to write algebraic proofs.
Identify properties of equality and
congruence.
Write two-column proofs.
Prove geometric theorems by using
deductive reasoning.
Write flowchart and paragraph
proofs.
Prove geometric theorems by using
Assessment
Resources
South Henry School Corporation ● Tri High School ● Straughn, Indiana
Curriculum Map
Course Title: Geometry
Quarter: 1
Academic Year: 2013-2014
Essential Questions for this Quarter:
1.
2.
3.
4.
5.
What is the correct terminology for basic geometric figures?
How can you apply basic formulas in and out of the coordinate plane?
How can you use inductive and deductive reasoning to make arguments?
How do you write and plan proofs?
How do you use properties of parallel lines and the angles formed by parallel lines and transversals?
Unit/Time Frame
Standards
Content
Skills





deductive reasoning.
Identify parallel, perpendicular, and
skew lines.
Identify the angles formed by two
lines and a transversal.
Prove and use theorems about the
angles formed by parallel lines and
a transversal.
Use the angles formed by a
transversal to prove two lines are
parallel.
Prove and apply theorems about
perpendicular lines.
Assessment
Resources
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
State Standards
G.1: Students find lengths and midpoints of line segments. They describe and use parallel and
perpendicular lines. They find slopes and equations of lines.
G.1.1: Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems.
G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines
using a straight edge and compass, explaining and justifying the process used.
G.1.3: Understand and use the relationships between special pairs of angles formed by parallel lines and
transversals.
G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.
G.2: Students identify and describe polygons and measure interior and exterior angles. They use
congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides,
perimeters, and areas.
G.2.2: Find measures of interior and exterior angles of polygons, justifying the method used.
G.2.3: Use properties of congruent and similar polygons to solve problems.
G.2.4: Apply transformations (slides, flips, turns, expansions, and contractions) to polygons in order to
determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips and
turns are congruent to the original shape.
G.2.5: Find and use measures of sides, perimeters, and areas of polygons, and relate these measures to
each other using formulas.
G.2.6: Use coordinate geometry to prove properties of polygons such as regularity, congruence, and
similarity.
G.3: Students identify and describe simple quadrilaterals. They use congruence and similarity. They
find measures of sides, perimeters, and areas.
G.3.1: Describe, classify, and understand relationships among the quadrilaterals square, rectangle,
rhombus, parallelogram, trapezoid, and kite.
G.3.2: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.
G.3.3: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures
to each other using formulas.
G.3.4: Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and
similarity.
G.4: Students identify and describe types of triangles. They identify and draw altitudes, medians,
and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters,
and areas. They apply inequality theorems.
G.4.1: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and
equiangular.
G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
G.4.3: Construct triangles congruent to given triangles.
G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.
G.4.5: Prove and apply theorems involving segments divided proportionally.
G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent
triangles.
G.4.7: Find and use measures of sides, perimeters, and areas of triangles, and relate these measures to
each other using formulas.
G.4.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle,
and hinge theorem.
G.4.9: Use coordinate geometry to prove properties of triangles such as regularity, congruence, and
similarity.
G.5: Students prove the Pythagorean Theorem and use it to solve problems. They define and apply
the trigonometric relations sine, cosine, and tangent.
G.5.1: Prove and use the Pythagorean Theorem.
G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right
triangle.
G.5.4: Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in
terms of angles of right triangles.
G.5.5: Know and use the relationship sin²x + cos²x = 1.
G.5.6: Solve word problems involving right triangles.
G.6: Students define ideas related to circles: e.g., radius, tangent. They find measures of angles,
lengths, and areas. They prove theorems about circles. They find equations of circles.
G.6.2: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and
tangent.
G.6.3: Prove theorems related to circles.
G.6.5: Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of
secants and tangents).
G.6.6: Define and identify congruent and concentric circles.
G.6.7: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use
these measures to solve problems.
G.6.8: Find the equation of a circle in the coordinate plane in terms of its center and radius.
G.7: Students describe and make polyhedra and other solids. They describe relationships and
symmetries, and use congruence and similarity.
G.7.2: Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given
polyhedron.
G.7.4: Describe symmetries of geometric solids.
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
G.7.5: Describe sets of points on spheres: chords, tangents, and great circles.
G.7.6: Identify and know properties of congruent and similar solids.
G.7.7: Find and use measures of sides, volumes of solids, and surface areas of solids, and relate these
measures to each other using formulas.
G.8: Mathematical Reasoning and Problem Solving
G.8.6: Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive
proof.
G.8.8: Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry.
Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, and twocolumn and indirect proofs.
Common Core Standards
Congruence G-CO
Experiment with transformations in the plane
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.
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).
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that
carry it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
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.
Understand congruence in terms of rigid motions
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.
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.
8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
Prove geometric theorems
9. Prove 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.
10. Prove 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.
11. Prove 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.
Make geometric constructions
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.
13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Similarity, Right Triangles, and Trigonometry G-SRT
Understand similarity in terms of similarity transformations
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.
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.
3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity
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.
5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
leading to definitions of trigonometric ratios for acute angles.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Apply trigonometry to general triangles
9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a
vertex perpendicular to the opposite side.
10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in
right and non-right triangles (e.g., surveying problems, resultant forces).
Circles G-C
Understand and apply theorems about circles
1. Prove that all circles are similar.
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.
3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
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.
Expressing Geometric Properties with Equations G-GPE
Translate between the geometric description and the equation for a
conic section
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.
2. Derive the equation of a parabola given a focus and directrix.
3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or
difference of distances from the foci is constant.
Use coordinates to prove simple geometric theorems algebraically
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).
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
5. Prove 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).
6. Find the point on a directed line segment between two given points that partitions the segment in a given
ratio.
7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the
distance formula.
Geometric Measurement and Dimension G-GMD
Explain volume formulas and use them to solve problems
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.
2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and
other solid figures.
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three dimensional
objects
4. Identify the shapes of two-dimensional cross-sections of three dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
Modeling with Geometry G-MG
Apply geometric concepts in modeling situations
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).
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square
mile, BTUs per cubic foot).
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).
Standards for Mathematical Practice
SMP1. Make sense of problems and persevere in solving them.
SMP2. Reason abstractly and quantitatively.
SMP3. Construct viable arguments and critique the reasoning of others.
SMP4. Model with mathematics.
SMP5. Use appropriate tools strategically.
SMP6. Attend to precision
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS
SMP7. Look for and make use of structure.
SMP8. Look for and express regularity in repeated reasoning.
South Henry School Corporation ● Tri High School ● Straughn, Indiana
COMMON CORE AND INDIANA ACADEMIC STANDARDS