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Grades 9/10/11 Measurement, Geometry, and Trigonometry
Pythagorean Theorem. Measurement of 2D figures and 3D solids. Optimization. Geometric relationships. Triangle trigonometry. Angles in standard position and trigonometric identities.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
Units
Unit 1: The Pythagorean Theorem, Measurement, and Optimization
Unit 2: Geometric Relationships
In this lesson, we will review properties of angles produced by intersecting lines (such as opposite, supplementary, and complementary angles). We will also review properties of angles produced by parallel lines and a transversal.
In this lesson, we will explore the properties and relationships of the interior and exterior angles of triangles, and use these relationships to solve angle problems. The ideas of conjectures and counterexamples are also introduced.
In this lesson, we will explore the properties and relationships of the interior and exterior angles of quadrilaterals and other polygons. We will apply these properties in solving angle problems and to verify conjectures.
In this lesson, we will investigate and describe properties of polygons. These properties will involve either the midpoints of the sides of the polygon, or the diagonals of the polygon.
In this lesson, we will discover some relationships between chords of circles and perpendicular bisectors. We will use the relationships we find to solve problems involving chords and perpendicular bisectors.
In this lesson, we will investigate the area of a sector and arc length. We will also investigate various properties about angles in a circle and use these properties to solve problems.
In this lesson, we will investigate the relationship between a tangent to a circle and the radius drawn to the point of tangency. We hope to discover a relationship and apply the relationship to solve problems.
All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.
This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.