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Course/Grade Levels Units

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Course Code
Content Area
The fundamental purpose of this course is to formalize and extend students’ geometric experiences from the earlier grades. Students will explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments.  They will prove theorems and solve problems about triangles, quadrilaterals, and other polygons; establish triangle congruence criteria based on analyses of rigid motions and formal constructions; apply similarity in right triangles to understand right triangle trigonometry; and use a rectangular coordinate system to verify geometric relationships. They will extend their knowledge of two-dimensional and three-dimensional objects to include informal explanations of circumference, area and volume formulas and consider the shapes of cross-sections.  Students will prove basic theorems about circles, and create and graph the equation of a circle.  They will use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities.

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Unit Description
GEOM01Basics of Geometry
Students will understand the defined and undefined terms of Geometry, analyze and apply transformations
to geometric figures and understand properties that are preserved by these transformations. They will construct geometric figures using a variety of tools and resources.
GEOM02Reasoning and Proofs
Students will be able to identify and prove angle relationships that occur with intersecting lines, perpendicular lines and parallel lines that are cut by a transversal.
GEOM03Parallel and Perpendicular Lines
Students will be able to determine if two triangles are congruent and, if so, complete a proof showing that
they are congruent.
The student will define midsegment, median, centroid, perpendicular and angle bisectors, and altitude
of triangles. They will apply and prove properties of these parts of triangles and use the coordinate plane to complete proofs.
GEOM05Congruent Triangles
Students will identify and apply similarity properties. They will prove polygons are similar/congruent, write
similarity statements, identify scale factors and use properties of similar triangles to solve application and algebraic problems.
GEOM06Relationships with Triangles
Students will solve problems that involve finding the missing sides and angles of a triangle using trigonometry and finding the area of an oblique triangle.
The student will derive and use the properties of special quadrilaterals utilizing geometric and algebraic concepts on a coordinate plane. They will be able to calculate the area and perimeter of polygons in the coordinate plane.
GEOM08Quadrilaterals and Other Polygons
Students will investigate and solve real-world problems involving area and volume.
GEOM09Right Triangles and Trigonometry
Students will discover the numerical relationship between arcs and angles of a circle and to provide ways of calculating segments related to circles.
Students will discover that all circles are similar and the proportionality of the length of an arc intercepted by an angle to the radius. Students will learn the origin of radians and its role as the constant of proportionality and derive the formula for the area of a sector. In addition, students use their prior algebraic understanding of the quadratic equation and Pythagorean Theorem to find the equation of a circle. Students will understand how to utilize the coordinate plane to determine whether a given point is on a circle.
GEOM11Circumference, Area, and Volume
Students will use conditional probability, represent sample space, use permutations and combinations,
and find probabilities of compound events.