MA.912.GR: Geometric Reasoning

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.

Concurrent Lines, Medians, and Altitudes
Investigating Angle Theorems
Parallel, Intersecting, and Skew Lines

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.

Congruence in Right Triangles
Proving Triangles Congruent
Similarity in Right Triangles

MA.912.GR.1.3: Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.

Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Segment and Angle Bisectors
Triangle Angle Sum
Triangle Inequalities

MA.912.GR.1.4: Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.

Parallelogram Conditions
Polygon Angle Sum
Special 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.

Classifying Quadrilaterals

MA.912.GR.1.6: Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.

Congruence in Right Triangles
Similar Figures
Similarity in Right Triangles

MA.912.GR.2.1: Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.

Dilations
Rotations, Reflections, and Translations
Translations

MA.912.GR.2.2: Identify transformations that do or do not preserve distance.

Dilations
Rotations, Reflections, and Translations
Translations

MA.912.GR.2.3: Specify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.

Rotations, Reflections, and Translations

MA.912.GR.2.5: Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.

Reflections
Rotations, Reflections, and Translations
Translations

MA.912.GR.2.7: Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.

Dilations

MA.912.GR.3.1: Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.

Circles

MA.912.GR.3.2: Solve geometric problems involving circles, triangles and quadrilaterals on the coordinate plane.

Circles

MA.912.GR.3.3: Solve mathematical and real-world problems on the coordinate plane that involve finding the coordinates of a point on a line segment including the midpoint.

Circles

MA.912.GR.3.4: Solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.

Distance Formula

MA.912.GR.4.1: Identify the shapes of two-dimensional cross-sections of three-dimensional figures.

Pyramids and Cones

MA.912.GR.4.2: Identify three-dimensional objects generated by rotations of two-dimensional figures.

Prisms and Cylinders
Pyramids and Cones

MA.912.GR.4.3: Determine how changes in dimensions affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MA.912.GR.4.4: Solve mathematical and real-world problems involving the area of two-dimensional figures.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles

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.

Prisms and Cylinders
Pyramids and Cones

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.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MA.912.GR.5.1: Construct a copy of a segment or an angle.

Constructing Congruent Segments and Angles

MA.912.GR.5.2: Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.

Constructing Parallel and Perpendicular Lines

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.

Chords and Arcs

MA.912.GR.6.2: Solve mathematical and real-world problems involving the measures of arcs and related angles, limited to central, inscribed and intersections of a chord, secants or tangents.

Chords and Arcs
Inscribed Angles

MA.912.GR.6.3: Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.

Inscribed Angles

MA.912.GR.6.4: Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.

Radians

MA.912.GR.6.5: Apply transformations to prove that all circles are similar.

Circles

MA.912.GR.7.2: Given a mathematical or real-world context, derive and create the equation of a circle using key features.

Circles

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.

Circles

MA.912.T: Trigonometry

MA.912.T.1.1: Define trigonometric ratios for acute angles in right triangles.

Sine, Cosine, and Tangent Ratios

MA.912.T.1.2: Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.

Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

MA.912.LT: Logic and Theory

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.

Biconditional Statements
Conditional Statements