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 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.


    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 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.


Last Modified on November 19, 2015