Course level: "Graduate"
"This course is designed for students to demonstrate the ability to use fundamental concepts of geometry including definitions, basic constructions, tools of geometry, and to recognize geometry as an axiomatic system. Students will apply theorems to evaluate various problems, analyze the properties of figures, and formulate equations utilizing geometric foundations."
Purchase of LabPaq® Hands-on Lab Kits are required for this course.
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What you'll learn
What you’ll learn
Foundations of Geometry and Conditional Statements
- Understand basic terms, measurement, and postulates of geometry on and off the coordinate plane.
- Investigate angles, including pairs of angles with special relationships.
- Illustrate basic constructions using a straightedge and compass.
- Apply the Angle Addition Postulate to find angle measures.
- Create conditional statements with their parts, including converse, inverse, contrapositive and bi-conditional.
- Prove geometric theorems using properties of equality.
Parallel and Perpendicular Lines and Congruence
- Apply theorems about parallel and perpendicular lines.
- Identify relationships between lines and planes that do not intersect.
- Prove that two lines are parallel or perpendicular.
- Identify corresponding parts in congruent figures.
- Prove triangle congruence using corresponding parts and SSS, SAS, ASA, and AAS postulates.
Quadrilaterals and Similar Polygons
- Analyze the properties of parallelograms.
- Analyze quadrilaterals using properties of diagonals.
- Solve problems involving proportional reasoning and theorems.
- Determine the area of quadrilaterals and triangles.
Pythagorean Theorem, Transformations, and Trigonometry Ratios
- Calculate areas of regular polygons.
- Differentiate between transformations of images.
- Apply the Pythagorean Theorem and properties of special triangles.
- Analyze the use of Sine, Cosine, and Tangent ratios to evaluate triangle problems.
- Evaluate problems involving law of sines and cosines.
- Investigate basics of circles.
- Investigate measures of angles, arcs, and chords related to circles.
- Explore the attributes of conics.
- Formulate the equation of various conics.
- Explore graphs of conics.
Review Topics and Objectives From All Weeks
- Review topics and objectives from all weeks.