Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.

MAT-10.GM.28 Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.

MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.

MAT-05.GM.G.02 Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.

MAT-05.GM.G.03 Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.

MAT-06.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.

MAT-06.GM.GF.02 Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.

MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.

MAT-10.GM.28Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.

MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.

MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given
complex number represent the same number.

MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.

MAT-12.NO.14 Recognize vector quantities as having both magnitude and direction, writing them in polar form.

MAT-12.NO.15 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

MAT-12.NO.16 Solve problems involving magnitude and direction that can be represented by vectors.

MAT-12.NO.17 Add and subtract vectors.

MAT-12.NO.18 Multiply a vector by a scalar.

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.

MAT-12.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.