Standards for Teaching and Learning
G.G.2: Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses).
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.
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.
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).
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.
G.G.11: Draw congruent and similar figures using a compass, straightedge, or protractor. Justify the constructions by logical argument.
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.
G.G.13: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.
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.
G.G.15: Use the properties of special triangles (e.g., isosceles, equilateral, 30º-60º-90º, 45º-45º-90º) to solve problems.
G.G.16: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
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.
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.
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.
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.
G.G.26: Use dimensional analysis for unit conversion and to confirm that expressions and equations make sense.
Correlation last revised: 3/1/2018