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
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