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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 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.