Download Academic Geometry and Trigonometry Syllabus

Boyertown Area School District
Course Syllabus
Course: Academic Geometry & Trigonometry
Grade: 9 - 10
Length of Course: Full year
Textbook(s): College Prep Mathematics (CPM) - Geometry Connections
Number of Periods per Cycle: 6
Course Description: This is an investigative, problem solving approach to understanding and applying geometric concepts including polygons,
circles, angles, lines, transformations, area, perimeter and proofs.
Course Outline
Quarter 1 Skills
Shapes and Transformations
 Describe how a change in one dimension of a figure
(2 or 3 dimensional) affects other measurements of
that figure.
 Locate points or describe relationships using the
coordinate plane.
 Identify and/or apply concepts of transformations or
symmetry
 Analyze characteristics and properties of two- and
three- dimensional geometric shapes and
demonstrate understanding of geometric
relationships
 Understand and/or apply basic concepts of
probability or outcomes
Angles and Measurement
 Use and/or compare measurements of angles.
 Use and/or develop procedures to determine or
describe measures of perimeter, circumference,
area, surface area and/or volume. (May require
conversions within the same system.)
 Recognize and/or apply properties of angles,
triangles and quadrilaterals.
 Identify special pairs of angles(supplementary,
complementary, adjacent, vertical and linear pair)
 Identify and use right angles and use perpendicular
lines
 Identify relationships between pairs of angles
formed by lines and transversals
 Use properties of parallel lines to determine angle
measures
Algebra
 Demonstrate an understanding of patterns, relations
and functions
 Compute and/or use the slope of a line
 Write, solve and/or graph linear equations and
inequalities using various methods
 Simplify expressions involving polynomials
Quarter 2 Skills
Triangle Similarity
 Recognize and/or apply properties of angles,
triangles and quadrilaterals
 Use properties of congruence, correspondence
and similarity in problem-solving settings
involving two- and three- dimensional figures
 Classify triangles by sides and angles
 Apply ratio and/or proportion in problemsolving situations
 Formulate or answer questions that can be
addressed with data and/or organize, display,
interpret or analyze data
Probability
 Apply probability and/or odds to practical
situations
 Develop and/or evaluate inferences and
predictions or draw conclusions based on data
or data displays
Right Triangles and Trigonometry
 Recognize and/or apply properties of angles,
triangles and quadrilaterals
 Solve problems involving right triangles using
the Pythagorean Theorem
 Use and apply sine, cosine and tangent to
solve right triangles
 Apply angles of elevation and depression to
trig problems
 Use law of sine and law of cosines in nonright triangles
 Use inverse trig functions to solve for angles
in a right triangle
Quarter 3 Skills
Right Triangles and Trigonometry
 Solve problems involving right triangles using
the Pythagorean Theorem
 Apply angles of elevation and depression to
trig problems
 Use law of sine and law of cosines in nonright triangles
 Use inverse trig functions to solve for angles
in a right triangle
Congruent Triangles
 Use properties of congruence, correspondence
and similarity in problem-solving settings
involving two- and three- dimensional figures
Proofs
 Represent and/or analyze mathematical
situations using numbers, symbols, words,
tables and/or graphs
 Use properties of congruence, correspondence
and similarity in problem-solving settings
involving two- and three- dimensional figures
 Appropriately display and/or use data in
problem-solving settings
Coordinate Geometry
 Interpret and/or use linear, quadratic and/or
exponential functions and their equations,
graphs or tables
 Compute and/or use the slope of a line
 Apply appropriate techniques, tools and
formulas to determine measurements
 Calculate midpoint of a segment
 Use all of the above to prove types of
quadrilaterals
Quarter 4 Skills
Circles



Identify and/or use parts of circles and segments associated
with circles
Analyze characteristics and properties of two- and threedimensional geometric shapes and demonstrate
understanding of geometric relationships
Use and/or develop procedures to determine or describe
measures of perimeter, circumference, area, surface area
and/or volume. (May require conversions within the same
system.)

Describe how a change in one dimension of a figure (2 or 3
dimensional) affects other measurements of that figure
Polygons
 Analyze characteristics and properties of two- and threedimensional geometric shapes and demonstrate
understanding of geometric relationships

Recognize and/or apply properties of angles, triangles and
quadrilaterals

Apply appropriate techniques, tools and formulas to
determine measurements
Area of Polygons

Use and/or develop procedures to determine or describe
measures of perimeter, circumference, area, surface area
and/or volume. (May require conversions within the same
system.)

Describe how a change in one dimension of a figure (2 or 3
dimensional) affects other measurements of that figure
Surface Area and Volume
 Use and/or develop procedures to determine or describe
measures of perimeter, circumference, area, surface area
and/or volume. (May require conversions within the same
system.)

Describe how a change in one dimension of a figure (2 or 3
dimensional) affects other measurements of that figure.

Apply appropriate techniques, tools and formulas to
determine measurements.
Circles
 Write the equation of a circle, working with parts of circles
Expected Value
 Calculate Expected Value
The assessment component(s) of this course include: tests, quizzes, mental math, homework, projects and other assignments.