MA19.GDA.35

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.35
Discover and apply relationships in similar right triangles.

Unpacked Content

Knowledge

Students know:

Techniques to construct similar triangles.
Properties of similar triangles.
Methods for finding sine and cosine ratios in a right triangle (e.g., use of triangle properties: similarity. Pythagorean Theorem. isosceles and equilateral characteristics for 45-45-90 and 30-60-90 triangles and technology for others).
Methods of using the trigonometric ratios to solve for sides or angles in a right triangle.
The Pythagorean Theorem and its use in solving for unknown parts of a right triangle.

Skills

Students are able to:

Accurately find the side ratios of triangles.
Explain and justify relationships between the side ratios of a right triangle and the angles of a right triangle.

Understanding

Students understand that:

The ratios of the sides of right triangles are dependent on the size of the angles of the triangle.
The sine of an angle is equal to the cosine of the complement of the angle.
Switching between using a given angle or its complement and between sine or cosine ratios may be used when solving contextual problems.

Vocabulary

Side ratios
Trigonometric ratios
Sine
Cosine
Tangent
Secant
Cosecant
Cotangent
Complementary anglesconverse

Aligned Learning Resources

"I Saw the Sine"

Collaborative Stories 1: Prewriting and Drafting

Why Is It Special?

Why is it Special? Verifying Relationships of Right Triangles

What Makes It Special? Remembering Relationships

Design by Adaptive Theme