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Course Code

MA.MA065S/MA066S

Content Area

Math

Description

This course is a rigorous proof-based course designed to develop spatial concepts and insight into geometric relationships. A precise mathematical language is developed with an emphasis on reading and real-life problem solving. Transformations on the coordinate plane provide opportunities for the formal study of congruence and similarity. The study of similarity leads to right triangle trigonometry and connects to quadratics and circles through Pythagorean relationships. The study of circles uses similarity and congruence to develop basic theorems related to circles and lines. The link between probability and data is explored through conditional probability. All units in this course will tie together geometric and previous advanced algebraic content knowledge such as systems of equations, factoring and solving quadratic equations. Advanced proofs are integrated throughout the course and will allow students to experience Geometry as a useful and logical subject.

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3|Math|1022|WG Honors Geometry

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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.

Students will be able to identify and prove angle relationships that occur with parallel lines that are cut by a transversal, intersecting lines and perpendicular lines.

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.

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.

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.

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.