#### MAT-10.GM.31

 10th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.

## Progressions

Circle Measurements

• MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply the given formula to calculate the area and circumference of a circle, including in authentic problems.
• MAT-10.GM.22 Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents, and chords to find unknown lengths or angles.
• MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-10.GM.31 Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
• MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
• MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
• MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.