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SENECA VALLEY SCHOOL DISTRICT
CURRICULUM
Course Title:
Course Number:
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Periods per Week:
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Date:
Geometry
0324
9
5
42 Minutes
Full Year
1.0
Mary McConaughy, Debbie Skinger
May 17, 2016
COURSE DESCRIPTION:
Geometry is an academically challenging course which includes an in-depth analysis of plane, solid, and coordinate
geometry as they relate to both abstract mathematical concepts, as well as real-world problem situations. Significant
emphasis is placed on algebra which is integrated throughout all units. The course is designed to focus on the key
topics of geometry including inductive reasoning, deductive reasoning and proofs, perpendicular and parallel lines,
triangles, quadrilaterals, proportions, right triangles and trigonometry, circles, surface area, and volume.
PREREQUITE(S): 70% or better in Algebra 1 OR 90% or better and teacher recommendation in Algebra 1B.
ESSENTIAL QUESTIONS:
1. How can patterns be used to describe relationships in mathematical situations?
2. How can recognizing repetition or regularity assist in solving problems more efficiently?
3. How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real
situations or solve problems?
4. How can the application of the attributes of geometric shapes support mathematical reasoning and problem solving?
5. How can geometric properties and theorems be used to describe, model, and analyze situations?
Geometry
–1–
COURSE OUTLINE
I.
OBJECTIVES (PA standard)
Tools of Geometry
A. Inductive Reasoning
Define and apply inductive reasoning to real-life situations
B. Number Patterns
Find the next term in number patterns
C. Picture Patterns
Draw the next picture in a sequence of picture patterns
D. Points, Lines & Planes
Use terminology and notation of points, lines and planes
Apply the postulates of Geometry
Use terminology and notation of segments, rays, parallel and
skew lines, and parallel planes
E. Measuring Segments &
Angles
Determine measures of segments and angles
Define and illustrate line and angle relationships
F.
Defining Line and Angle
Relationships
Define and classify polygons and related terms
G. Defining Polygons
Define and classify triangles and their related parts
H. Defining Triangles
Define and classify special quadrilaterals and their related parts
I.
J.
Defining Special
Quadrilaterals
Solve statement problems by first translating each into a labeled
diagram
Translating Word
Problems into Diagrams
Geometry
–2–
COURSE OUTLINE
OBJECTIVES (PA standard)
II. Geometric Construction
A. Constructing
Perpendicular Bisectors
Construct perpendicular bisectors given a line segment
B. Construct Perpendiculars
Construct perpendicular lines given a point on a line and a point
not on a line
C. Construct Angle Bisectors
Construct angle bisectors
D. Construct Medians,
Altitudes, and Angle
Bisectors in Triangles
Construct medians, altitudes, and angle bisectors in triangles
Geometry
–3–
COURSE OUTLINE
OBJECTIVES (PA standard)
III. Exploring Geometry
A. Discovering Angle
Relationships
B. Triangle Sum Conjecture
C. Polygon Sum Conjecture
D. Exterior Angles of a
Polygon
E. Triangle Inequalities
F.
Properties of Isosceles
Triangles
G. Properties of Parallel
Lines
Use properties of angles formed by intersecting lines to find
the measures of missing angles. (G.2.2.1.1) CC.2.3.HS.A.3
To find missing angle measures by using linear pair and vertical
angles conjectures.
Identify and/or use properties of triangles. (G.1.2.1.1)
CC.2.3.HS.A.3, CC.2.3.HS.A.13
Solve problems by applying the triangle sum conjecture.
Identify and/or use properties of regular polygons.
(G.1.2.1.4) CC.2.3.HS.A.3, CC.2.3.HS.A.13
Solve problems by applying the polygon exterior sum
conjecture.
Identify and/or use properties of triangles. (G.1.2.1.1)
CC.2.3.HS.A.3, CC.2.3.HS.A.13
Determine and apply the triangle inequality conjecture.
Identify and/or use properties of isosceles and equilateral
triangles. (G.1.2.1.3) CC.2.3.HS.A.3, CC.2.3.HS.A.13
Use properties of angles formed when two parallel lines are
cut by a transversal to find the measures of missing angles.
(G.2.2.1.2) CC.2.3.HS.A.3
Geometry
–4–
COURSE OUTLINE
IV. Special Quadrilaterals
OBJECTIVES (PA standard)
Identify and/or use properties of quadrilaterals. (G.1.2.1.2)
CC.2.3.HS.A.3, CC.2.3.HS.A.13
A. Properties of Trapezoids
Apply properties of trapezoids.
B. Properties of Mid-segments
Apply properties of mid-segments in triangles and trapezoids.
C. Properties of
Parallelograms
D. Properties of Special
Parallelograms
Apply properties of parallelograms.
Apply properties of rectangles, rhombi and squares.
Geometry
–5–
COURSE OUTLINE
V. Congruent Triangles
A. Congruent Figures
B. Triangle Congruence by
SSS and AAA?
C. Triangle Congruence by
SAS and SSA?
D. Triangle Congruence by
ASA and AAS?
E. Using Congruent
Triangles: CPCTC
F.
OBJECTIVES (PA standard)
Identify and/or use properties of congruent and similar
polygons or solids. (G.1.3.1.1) CC.2.3.HS.A.2,
CC.2.3.HS.A.5, CC.2.3.HS.A.6
Define and apply congruent polygons, segments and angles.
Determine congruent triangles by Side-Side-Side Congruence
Conjecture.
Determine congruent triangles by Side-Angle-Side Congruence
Conjecture.
Determine congruent triangles by Angle-Side-Angle and AngleAngle-Side Congruence Conjectures.
Overlapping Triangles
Determine whether segments or angles are congruent by using
CPCTC.
Determine congruent triangles by SSS, SAS, ASA and AAS
Congruence Conjectures in overlapping triangles.
Geometry
–6–
COURSE OUTLINE
VI. Deductive Reasoning &
Geometric Proof
A. Deductive Reasoning
B. Premises of Geometry
OBJECTIVES (PA standard)
Identify and/or use properties of triangles. (G.1.2.1.1)
CC.2.3.HS.A.3, CC.2.3.HS.A.13
Write, analyze, complete, or identify formal proofs (e.g.,
direct and/or indirect proofs/proofs by contradiction).
(G.1.3.2.1) CC.2.3.HS.A.3, CC.2.3.HS.A.6, CC.2.3.HS.A.8,
2.2.HS.C.9
C. Algebraic Proofs
D. Proving Angle Pair
Relationships
E. Proving Properties of
Parallel Lines
F.
Proving Parallel Lines
G. Proving Congruent
Triangles
H. Using CPCTC in Proofs
I.
Using Overlapping
Triangles in Proofs
J.
Indirect Proofs
Define and apply deductive reasoning to real-life situations.
Draw conclusions from given information and justify these
using premises (definitions and undefined terms, properties of
algebra, equality, and congruence, postulates of geometry, and
previously accepted/proven geometric theorems for geometric
arguments
Write simple algebraic proofs
Prove and apply theorems about angles and their corollaries.
(Vertical Angles, Congruent Supplements, and Congruent
Complements theorems, and their corollaries)
Prove and apply properties of parallel lines intersected by a
transversal. (Alternate Interior Angles Theorem, Alternate
Exterior Angles Theorem, Same-Side Interior Angles Theorem,
Same-Side Exterior Angles Theorem)
Prove lines parallel. (Converses of the Alternate Interior Angles
Theorem, Alternate Exterior Angles Theorem, Same-Side
Interior Angles Theorem, Same-Side Exterior Angles Theorem)
Prove two triangles congruent using SSS, SAS, ASA, and AAS
Congruence Postulates.
Prove that parts of two triangles are congruent using triangle
congruence and CPCTC
Prove two triangles or parts congruent in overlapping triangles.
Write indirect proofs
Geometry
–7–
COURSE OUTLINE
VII. Circles
A. Circle Parts
B. Properties of Chords, Arcs
& Central Angles
OBJECTIVES (PA standard)
Identify, determine, and/or use the radius, diameter,
segment, and/or tangent of a circle. (G.1.1.1.1)
CC.2.3.HS.A.8, CC.2.3.HS.A.9, CC.2.3.HS.A.13
Identify, determine, and/or use the arcs, semicircles, sectors,
and/or angles of a circle. (G.1.1.1.2) CC.2.3.HS.A.8,
CC.2.3.HS.A.9, CC.2.3.HS.A.13
C. Tangent Properties
D. Inscribed Angles & their
Intercepted Arcs
Use chords, tangents, and secants to find missing arc
measures or missing segment measures. (G.1.1.1.3)
CC.2.3.HS.A.8, CC.2.3.HS.A.9, CC.2.3.HS.A.13
E. Circumference/Diameter
Ratio
Define, identify and use proper notation for circles and their
parts
F.
Determine and apply properties of chords, arcs and central
angles in circles
Arc Length
G. Other Angle Relationships
in Circles
H. Segment Lengths in
Circles
Determine and apply properties of tangents in circles (Tangent
Theorem and Tangent Segments Theorem)
Apply properties of inscribed angles and their intercepted arcs in
circles
Find the area and circumference of a circle. Solve problems
involving area and circumference of a circle(s). (M07.CG.2.2.1) CC.2.3.7.A.1
Define and apply arc length theorem
Find the measures of angles formed by chords, secants and
tangents
Find the lengths of segments associated with circles
Geometry
–8–
COURSE OUTLINE
VIII. Area and Surface Area
A. Areas of Rectangles and
Parallelograms
OBJECTIVES (PA standard)
Determine the area of triangles and special quadrilaterals
(i.e., square, rectangle, parallelogram, rhombus, and
trapezoid. (M06.C-G.1.1.1) CC.2.3.6.A.1
B. Areas of Triangles and
Trapezoids
Find the measurement of a missing length, given the
perimeter, circumference, or area. (G.2.2.2.2)
CC.2.3.HS.A.3, CC.2.3.HS.A.9, CC.2.3.HS.C.1
C. Areas of Regular
Polygons
Solve multi-step problems involving area and perimeter of
rectangles and parallelograms
D. Areas of Circles
Solve multi-step problems involving area and perimeter of
triangles and trapezoids
E. Areas of a Sector, a
Segment and an Annulus
F.
Irregular Areas
G. Surface Area of Prisms,
Pyramids, Cones,
Cylinders and Spheres
H. Maximizing Area
I.
J.
Solve multi-step problems involving area and perimeter of
regular polygons
Changing Values in
Linear Dimension
Geometric Probability
Find the area and circumference of a circle. Solve problems
involving area and circumference of a circle(s). (M07.CG.2.2.1) CC.2.3.7.A.1
Find the area of the sector of a circle. (G.2.2.2.5)
CC.2.3.HS.A.3, CC.2.3.HS.A.9, CC.2.3.HS.C.1
Find the area of circle portions (sector, segment and annulus)
Develop and/or use strategies to estimate the area of a
compound/composite figure. (G.2.2.2.4) CC.2.3.HS.A.3,
CC.2.3.HS.A.9, CC.2.3.HS.C.1
Estimate area, perimeter, or circumference of an irregular
figure. (G.2.2.2.1) CC.2.3.HS.A.3, CC.2.3.HS.A.9,
CC.2.3.HS.C.1
Calculate the surface area of prisms, cylinders, cones,
pyramids, and/or spheres. Formulas are provided on a
reference sheet. (G.2.3.1.1) CC.2.3.HS.A.14, CC.2.3.HS.A.12
Find the measurement of a missing length, given the surface
area or volume. (G.2.3.1.3) CC.2.3.HS.A.14, CC.2.3.HS.A.12
Find the side lengths of a polygon with a given perimeter to
maximize the area of the polygon. (G.2.2.2.3) CC.2.3.HS.A.3,
Geometry
–9–
COURSE OUTLINE
OBJECTIVES (PA standard)
CC.2.3.HS.A.9, CC.2.3.HS.C.1
Describe how a change in the linear dimension of a figure
affects its perimeter, circumference, and area. (G.2.2.3.1)
CC.2.3.HS.A.9, CC.2.3.HS.A.8
Describe how a change in the linear dimension of a figure
affects its surface area or volume. (G.2.3.2.1)
CC.2.3.HS.A.13
Use area models to find probabilities. (G.2.2.4.1)
CC.2.3.HS.A.14
Geometry
–10–
OBJECTIVES (PA standard)
COURSE OUTLINE
IX. Right Triangles
A. Simplifying, Multiplying
& Rationalizing Radicals
Simplify radicals
Multiply radicals
Rationalize radicals
B. The Pythagorean Theorem
and Its Converse
C. Pythagorean Primitives
and their Multiples
D. Isosceles Right and
30-60-90 triangles
E. Right Triangle
Application
Use the Pythagorean theorem to write and/or solve problems
involving right triangles. (G.2.1.1.1) CC.2.3.HS.A.7,
CC.2.2.HS.C.9
Use the Pythagorean primitives and their multiples to determine
unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions
Use isosceles right triangles and 30-60-90 triangles to determine
unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions
Apply the Pythagorean Theorem to determine unknown side
lengths in right triangles in real-world and mathematical
problems in two and three dimensions. (M08.C-G.2.1.2)
CC.2.3.8.A.3
Geometry
–11–
COURSE OUTLINE
OBJECTIVES (PA standard)
X. Volume
A. Classifying Polyhedrons
Classify polyhedrons by their number of faces
Determine and use Euler’s Formula
B. Prisms & Pyramids
Identify and/or use properties of pyramids and prisms.
(G.1.2.1.5) CC.2.3.HS.A.3, CC.2.3.HS.A.13
C. Solids with Curved
Surfaces
Identify and/or use the properties of a sphere or cylinder.
(G.1.1.1.4) CC.2.3.HS.A.8, CC.2.3.HS.A.9, CC.2.3.HS.A.13
D. Volumes of Prisms and
Cylinders
D-F: Calculate the volume of prisms, cylinders, cones,
pyramids, and/or spheres. (G.2.3.1.2) CC.2.3.HS.A.14,
CC.2.3.HS.A.12
E. Volumes of Pyramids and
Cones
F.
Volumes of Spheres
G. Changing Values in
Linear Dimension
D-F: Find the measurement of a missing length, given the
surface area or volume. (G.2.3.1.3) CC.2.3.HS.A.14,
CC.2.3.HS.A.12
Describe how a change in the linear dimension of a figure
affects its surface area or volume. (G.2.3.2.1)
CC.2.3.HS.A.13
Geometry
–12–
COURSE OUTLINE
OBJECTIVES (PA standard)
XI. Similarity
A. Using Ratios and
Proportions
Use ratios and proportions to solve real-life applications
B. Similar Polygons
B-C: Identify and/or use properties of congruent and similar
polygons or solids. (G.1.3.1.1) CC.2.3.HS.A.2,
CC.2.3.HS.A.5, CC.2.3.HS.A.6
C. Proving Triangles Similar
D. Indirect Measurement
E. Corresponding Parts of
Similar Triangles
F.
Perimeter, Area and
Volume of Similar
Figures
D-E: Identify and/or use proportional relationships in
similar figures. (G.1.3.1.2) CC.2.3.HS.A.2, CC.2.3.HS.A.5,
CC.2.3.HS.A.6
Identify and/or use properties of congruent and similar
polygons or solids. (G.1.3.1.1) CC.2.3.HS.A.2,
CC.2.3.HS.A.5, CC.2.3.HS.A.6
Geometry
–13–
COURSE OUTLINE
OBJECTIVES (PA standard)
XII. Trigonometry
A. Trigonometric Ratios
Use trigonometric ratios to write and/or solve problems
involving right triangles. (G.2.1.1.2) CC.2.3.HS.A.7,
CC.2.2.HS.C.9
Geometry
–14–
COURSE OUTLINE
OBJECTIVES (PA standard)
XIII. Coordinate Geometry
A. Distance Formula
A-B: Calculate distance and a midpoint algebraically.
(G.2.1.2.1) CC.2.3.HS.A.11
B. Midpoint Formula
C. The Slope of a Line
C-D: Relate slope to perpendicularity and/or parallelism.
(G.2.1.2.2) CC.2.3.HS.A.11
D. Slope of Parallel and
Perpendicular Lines
E. Classifying Quadrilaterals
by Coordinate Methods
Use slope, distance, and/or midpoint between two points on a
coordinate plane to establish properties of a 2-dimensional
shape. (G.2.1.2.3) CC.2.3.HS.A.11
Geometry
–15–