Download To View and Print the Course Syllabus PDF

Rogers High School
Geometry Course Syllabus
2015 – 2016
QUARTER 1
Unit 1.1: Defining Geometry Vocabulary
 Differentiate between Euclidean and non-Euclidean geometry.
 Discuss point, line, and plane and distance along the line.
 Define angle.
 Define parallel and perpendicular lines.
Unit 1.2: Making Geometric Constructions
 Use paper, pencil, straightedge, and compass to copy and bisect a segment, to
copy and bisect an angle, and to construct a perpendicular line. Create a
detailed explanation of each process.
 Use software to copy segments, bisect segments and angles; and construct
perpendicular lines. Explain each process.
Unit 1.3: Working with Transformations
 Describe which movements put rectangles, parallelograms, trapezoids, or
regular polygons onto themselves.
 Develop definitions of rotations, reflections, and translations.
 Draw a transformed figure from a given description.
 Describe transformations that create a given image.
 Describe transformations as functions.
 Represent a transformation from function notation.
 Use transparencies to show the transformations from original to final placing.
Unit 1.4: Proving Geometric Theorems
 Understand how proofs can be written in a variety of ways.
 Construct and prove the Perpendicular Bisector Theorem and then construct a
line parallel to a given line through a point not on the line.
 Prove vertical angles are always congruent, and that alternate interior and
corresponding angles are congruent when a transversal crosses parallel lines.
 Prove the Triangle Sum Theorem, the Base Angles Theorem, the Midsegment
Theorem, and prove medians of a triangle meet at a point.
QUARTER 2
Unit 2.1: Proving Triangle Congruence
 Experiment with rigid motion and predict effect on a given figure.
 Develop a definition of congruence between two figures.
 Experiment and develop SSS, SAS, and ASA triangle congruence criteria.
 Use SSS, SAS, and ASA to explain if triangles are congruent.
 Solve problems involving congruent triangles.
Unit 2.2: Using Slope to Solve Geometric Problems
 Prove slope criteria for parallel and perpendicular lines.
 Find equations of lines (parallel/perpendicular) to a given line through a given
point.
 Prove the distance formula using Pythagorean Theorem.
 Use parallel and perpendicular lines along with the distance formula to solve
geometric problems.
Unit 2.3: Proving Theorems About Parallelograms
 Prove opposite sides of a parallelogram are congruent.
 Prove diagonals of a parallelogram bisect each other.
 Prove opposite angles of a parallelogram are congruent.
 Prove rectangles are parallelograms with congruent diagonals.
 Use coordinate plane to determine if any four given vertices form a
parallelogram, rectangle, or neither.
Unit 2.4: Computing Perimeters and Areas of Polygons
 Use coordinates, the distance formula, and Pythagorean Theorem to prove
perimeters of polygons algebraically.
 Use coordinates, the distance formula, and Pythagorean Theorem to prove the
areas of triangles algebraically.
 Use coordinates, the distance formula, and Pythagorean Theorem to prove the
areas of rectangles algebraically.
Quarter 3
Unit 3.1: Verifying Properties of Dilations
 Experiment with Geometry software and dilation.
 Develop properties of dilations.
 Discuss scale factor and perform operations.
 Use transformations to increase understanding of similarity.
Unit 3.2: Understanding Similarity through Transformations
 Define similarity using transformations.
 Using similarity, explain transformations and the meaning of similarity for
triangles.
 Establish AA criteria using properties of similarity for triangles.
 Determine if two given triangles are similar.
 Apply properties of similar triangles to solve problems and justify conclusions.
Unit 3.3: Proving Theorems Involving the Pythagorean Theorem
 Experiment using software, paper, and pencil with triangles and parallel lines.
 Prove triangle proportionality theorems and its converse.
 Prove the Pythagorean Theorem and its converse, using triangle similarity.
 Use coordinates to prove simple geometric theorems algebraically.
 Apply congruence and similarity criteria of triangles to solve problems.
Unit 3.4: Understanding Trigonometry and Solving Real-World Problems
 Define trigonometric ratios for acute angles in right triangles, using similarity
and side length.
 Understand that the sine and cosine of complementary angles are equivalent.
 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles
for real world applications.
 Apply geometric methods to solve design problems.
Quarter 4
Unit 4.1: Modeling and Identifying Three-Dimensional Figures
 Visualize relationships between two and three-dimensional objects.
 Identify three-dimensional objects and their cross sections.
 Identify three-dimensional objects generated by rotating a two-dimensional
object.
 Use the properties of two and three-dimensional objects to identify a threedimensional shape in the real world.
Unit 4.2: Giving Informal Argument for Formulas and Solving Real-World
Problems Using Volume Formulas
 Discuss distance along circular arc and define circle.
 Given an informal argument for circumference and area of a circle.
 Given an informal argument for volume of a cylinder and a cone.
 Given an informal argument for volume of a pyramid.
 Solve problems using volume formulas in the real world.
 Apply concepts of area, volume, and density in modeling situations.
Unit 4.3: Identifying and Describing Relationships among Circle Angles and
Segments and Applying Theorems about Circles
 Identify angles, radii, and chords in a circle.
 Describe relationships among angles, radii, and chords.
 Construct an equilateral triangle, square, and regular hexagon inscribed in a
circle and circumscribe a triangle.
 Construct inscribed and circumscribed triangles in a circle.
 Prove properties of angles for a quadrilateral inscribed in a circle.
 Use similarity to derive the fact that arc length is proportional to the radius.
 Define radian measure and the formula for the area of a sector.
 ·Use coordinates to prove or disprove that a point lies on a circle with a given
radius.
Unit 4.4: Deriving the Equation of a Circle and Proving that all Circles are Similar
 Derive the equation of a circle of given center and radius using the
Pythagorean Theorem.
 Complete the square of a quadratic equation to find the center and radius of a
circle given by an equation.
 Prove that all circles are similar.