Rogers High School
Geometry Course Syllabus
2015 – 2016
Unit 1.1: Defining Geometry Vocabulary
Differentiate between Euclidean and non-Euclidean geometry.
Discuss point, line, and plane and distance along the line.
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.
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.
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.
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 three-dimensional 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.