## Geometry Content & Skills

#### Geometry Pre-Requisite Content and Skills

Pre-Requisite Expectations
• Solve linear equations in one variable with coefficients represented by real numbers and variables (A-REI.3)
• Solve quadratic equations in one variable using factoring, completing the square, and quadratic formula (A-REI.4)
Solving equations tutorials   Quadratic Equations tutorials   Middle School Geometry content/skills Pre-Requisite Expectations
• Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes (6.G.1)
• Use the formulas for the area and circumference of a circle to solve problems (7.G.4)
• Solve real-world and mathematical problems involving volume of three-dimensional shapes composed of cubes and right prisms (7.G.6)
• Use the Pythagorean Theorem to determine unknown side lengths (8.G.7)
• Use the volume of cones, spheres, and cylinders to solve real-world and mathematical problems (8.G.9)
Middle school geometry tutorials

#### Modeling with Geometry Unit

Learning Expectations
• Make formal constructions with a variety of tools and methods (for example compass, straightedge, string, reflective devices, paper folding, software) (G-CO.12)
• Know precise definitions of angle and line segment based on the undefined notions of point, line, plane, and distance along a line (length of a segment) (G-CO.1)
Modeling with Geometry tutorials

#### Rigid Motions Unit

Learning Expectations
• Verify experimentally that a dilation of a line segment is longer or shorter in the ration given by the scale factor (G-SRT.1b)
• Describe the rotations and reflections that carry a given rectangle, parallelogram, trapezoid or regular polygon onto itself (G-CO.3)
• Develop definitions of rotations, reflections, and translations (G-CO.4)
• Specify the sequence of transformations that will carry a given figure onto another (G-CO.2)
• Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure (G-CO.6)
Rigid motions tutorials

#### Geometric Relationships and Properties Unit

Learning Expectations
• Know the precise definition of perpendicular line and parallel line based on the undefined notions of point, line, plane, and distance along a line (length of a segment) (G-CO.1)
• Develop an understanding of conditionals, converses, and definitions and how they are used in proofs (G-CO-Fairfield.1)
• Prove theorems about lines and angles (G-CO.9)
• Prove theorems about triangles (G-CO.10)
• Prove theorems about parallelograms (G-CO.11)
• Show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are also congruent (G-CO.7)
• Explain how the criteria for triangle congruence (ASA, SAS, & SSS) follow from the definition of congruence in terms of rigid motions (G-CO.8)
Geometric properties tutorials

#### Coordinate Geometry Unit

Learning Expectations
• Use the slop criteria of parallel and perpendicular lines to solve geometric problems (G-GPE.5)
• Use coordinates to prove simple geometric theorems algebraically (G-GPE.4)
• Use coordinates to compute perimeters and areas of triangles and rectangles (G-GPE.7)
Coordinate geometry tutorials

#### Similarity Unit

Learning Expectations
• Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures (G-SRT.5)
• Determine if two figures are similar using transformations (G-SRT.2)
• Establish the AA criterion for two triangles to be similar using the properties of similarity transformations (G-SRT.3)
• Explain, suing similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides (G-SRT.2)
Similarity tutorials

#### Trigonometric Ratios Unit

Learning Expectations
• Use trigonometric rations and the Pythagorean Theorem to solve right triangles in applied problems (G-SRT.8)
• Understand that by similarity, side ratios in right triangles are properties of the acute angles of the right triangles, lead to definitions of trigonometric ratios (G-SRT.6)
• Explain the relationship between the sine and cosine of complementary angles (G-SRT.7)
• Find the missing sides of special right triangles (30-60-90 & 45-45-90) given two sides (G-SRT-Fairfield.1)
• Apply the Laws of Sines & Cosines to find unknown measurements in right and non-right triangles (G-SRT.11) – Only in Geometry-21
Trigonometric ratios tutorials

#### Geometric Measurement and Dimension Unit

Learning Expectations
• Use the volume formulas for cylinders, pyramids, cones, and spheres to solve problems (G-GMD.3)
• Give informal arguments for the formulas for the circumference of a circle, area of a circle and the volume of a cylinder, pyramid, and cone (G-GMD.1)
• Find the area of regular polygons (G-SRT-Fairfield.2)
• Identify three-dimensional objects generated by rotations of two-dimensional objects (G-GMD.4)
• Identify shapes of two-dimensional cross sections of three-dimensional objects (G-GMD.4)
Geometric measurements and dimension tutorials