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### GR Geometric Reasoning

- MA.912.GR.1 Prove and apply geometric theorems to solve problems.
- MA.912.GR.1.1 Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.
- MA.912.GR.1.2 Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
- MA.912.GR.1.3 Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
- MA.912.GR.1.4 Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.
- MA.912.GR.1.5 Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.
- MA.912.GR.1.6 Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
- Checkpoint opportunity

- MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.
- MA.912.GR.2.1 Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.
- MA.912.GR.2.2 Identify transformations that do or do not preserve distance.
- MA.912.GR.2.3 Identify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
- MA.912.GR.2.5 Given a geometric figure and a sequence of transformations, draw the transformed figure on a coordinate plane.
- MA.912.GR.2.6 Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
- MA.912.GR.2.8 Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
- Checkpoint opportunity

- MA.912.GR.3 Use coordinate geometry to solve problems or prove relationships.
- MA.912.GR.3.1 Determine the weighted average of two or more points on a line.
- MA.912.GR.3.2 Given a mathematical context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.
- MA.912.GR.3.3 Use coordinate geometry to solve mathematical and real-world geometric problems involving lines, circles, triangles and quadrilaterals.
- MA.912.GR.3.4 Use coordinate geometry to solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
- Checkpoint opportunity

- MA.912.GR.4 Use geometric measurement and dimensions to solve problems.
- MA.912.GR.4.1 Identify the shapes of two-dimensional cross-sections of three-dimensional figures.
- MA.912.GR.4.2 Identify three-dimensional objects generated by rotations of two-dimensional figures.
- MA.912.GR.4.3 Extend previous understanding of scale drawings and scale factors to determine how dilations affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
- MA.912.GR.4.4 Solve mathematical and real-world problems involving the area of two-dimensional figures.
- MA.912.GR.4.5 Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
- MA.912.GR.4.6 Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
- Checkpoint opportunity

- MA.912.GR.5 Make formal geometric constructions with a variety of tools and methods.
- MA.912.GR.5.1 Construct a copy of a segment or an angle.
- MA.912.GR.5.2 Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.
- MA.912.GR.5.3 Construct the inscribed and circumscribed circles of a triangle.
- Checkpoint opportunity

- MA.912.GR.6 Use properties and theorems related to circles.
- MA.912.GR.6.1 Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.
- MA.912.GR.6.2 Solve mathematical and real-world problems involving the measures of arcs and related angles.
- MA.912.GR.6.3 Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
- MA.912.GR.6.4 Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.
- Checkpoint opportunity

- MA.912.GR.7 Apply geometric and algebraic representations of conic sections.
- MA.912.GR.7.2 Given a mathematical or real-world context, derive and create the equation of a circle using key features.
- MA.912.GR.7.3 Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.
- Checkpoint opportunity

### T Trigonometry

- MA.912.T.1 Define and use trigonometric ratios, identities or functions to solve problems.
- MA.912.T.1.1 Define trigonometric ratios for acute angles in right triangles.
- MA.912.T.1.2 Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
- Checkpoint opportunity

### LT Logic and Discrete Theory

- MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
- MA.912.LT.4.3 Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.
- MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.