Standards for Teaching and Learning
G.G.2: Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses).
Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms
G.G.3: Apply properties of sides, diagonals, and angles in special polygons; identify their parts and special segments (e.g., altitudes, midsegments); determine interior angles for regular polygons.
G.G.4: Draw and label sets of points such as line segments, rays, and circles.
Parallel, Intersecting, and Skew Lines
G.G.5: Detect symmetries of geometric figures.
G.G.6: Apply the triangle inequality and other inequalities associated with triangles (e.g., the longest side is opposite the greatest angle) to prove theorems and to solve problems.
G.G.7: Use properties and theorems about congruent and similar figures and about perpendicular and parallel lines to solve problems.
Constructing Congruent Segments and Angles
Similar Figures
G.G.8: Write simple proofs of theorems in geometric situations, such as theorems about triangles, congruent and similar figures, and perpendicular and parallel lines (e.g., the longest side is opposite the greatest angle, two lines parallel to a third are parallel to each other; perpendicular bisectors of line segments are the set of all points equidistant from the two end points).
Investigating Angle Theorems
Isosceles and Equilateral Triangles
Similar Figures
Triangle Angle Sum
Triangle Inequalities
G.G.9: Distinguish between postulates and theorems. Use inductive and deductive reasoning, as well as proof by contradiction. Given a conditional statement, write its inverse, converse, and contrapositive.
Biconditional Statements
Conditional Statements
G.G.11: Draw congruent and similar figures using a compass, straightedge, or protractor. Justify the constructions by logical argument.
Constructing Congruent Segments and Angles
G.G.12: Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles
G.G.13: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.
Chords and Arcs
Constructing Congruent Segments and Angles
Inscribed Angles
Parallel, Intersecting, and Skew Lines
G.G.14: Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem; study and understand more than one proof of this theorem.
Circles
Cosine Function
Distance Formula
Isosceles and Equilateral Triangles
Polygon Angle Sum
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function
Triangle Angle Sum
G.G.15: Use the properties of special triangles (e.g., isosceles, equilateral, 30º-60º-90º, 45º-45º-90º) to solve problems.
Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Cosine Function
Isosceles and Equilateral Triangles
Sine Function
Tangent Function
Triangle Inequalities
G.G.16: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
Sine, Cosine, and Tangent Ratios
G.G.17: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope.
Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
G.G.18: Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems.
Points in the Coordinate Plane
Slope
Slope-Intercept Form of a Line
G.G.20: Draw the results and interpret transformations on figures in the coordinate plane such as translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.
Dilations
Rotations, Reflections, and Translations
Translations
G.G.22: Find and use measures of perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
G.G.23: Find and use measures of lateral areas, surface areas, and volumes of prisms, pyramids, spheres, cylinders, and cones, and relate these measures to each other using formulas.
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
G.G.26: Use dimensional analysis for unit conversion and to confirm that expressions and equations make sense.
Correlation last revised: 5/9/2018