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.09 Prove and apply theorems about lines and angles.

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

MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).

MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.

MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.

MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.

MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying
facts about these angles.

MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.

MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.

MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.

MAT-10.GM.09 Prove and apply theorems about lines and angles.

MAT-10.GM.10 Prove and apply theorems about triangles.

MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.

MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.

MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).

MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.

MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.

MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.

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-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.

MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.

MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context