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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
Unit 3: Trigonometry
In this lesson, we review the concepts of congruence and similarity. We also learn how to compute the scale factor relating similar polygons and use this to solve problems involving perimeter and area.
In this lesson, we review the angle-angle (AA), side-angle-side (SAS), and side-side-side (SSS) similarity rules for demonstrating that two triangles are similar. We next use similar triangle constructions to solve a variety of problems.
In this lesson, we will define the tangent ratio and see how to use it to solve a variety of problems involving right-angled triangles. We will also learn how to use the inverse tangent operation to solve for an interior angle in a right-angled triangle.
In this lesson, we define the sine and cosine ratios and use them to solve a variety of problems involving right-angled triangles. We also learn how to perform calculations involving sine and cosine operations using calculators.
In this lesson, we state and prove the sine law for acute triangles. We then use the sine law to determine side lengths and angles in acute triangles.
In this lesson, we derive the cosine law for acute triangles. We then use the cosine law to determine side lengths and angles in acute triangles.
In this lesson, we review the sine and cosine laws and under what conditions they can be used. We also apply the sine and cosine laws to solve a variety of application-style problems.
In this lesson, we learn how to compute the sine, cosine, and tangent ratios corresponding to oblique angles and vice versa. We see that determining the oblique angle associated with a given sine ratio can give rise to ambiguities. This leads into a discussion of the ambiguous case of the sine law.
In this lesson, we use trigonometric tools developed for two-dimensional right-angled and oblique triangles to solve problems in three-dimensional settings.
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.