111.34.G.2: The student analyzes geometric relationships in order to make and verify conjectures.

111.34.G.2.A: use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and

111.34.G.3: The student applies logical reasoning to justify and prove mathematical statements.

111.34.G.3.A: determine the validity of a conditional statement, its converse, inverse, and contrapositive;

111.34.G.3.B: construct and justify statements about geometric figures and their properties;

111.34.G.5: The student uses a variety of representations to describe geometric relationships and solve problems.

111.34.G.5.A: use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

111.34.G.5.B: use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

111.34.G.5.D: identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

111.34.G.6: The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

111.34.G.6.B: use nets to represent and construct three-dimensional geometric figures; and

111.34.G.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

111.34.G.7: The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

111.34.G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

111.34.G.7.B: use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and

111.34.G.7.C: derive and use formulas involving length, slope, and midpoint.

111.34.G.8: The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

111.34.G.8.A: find areas of regular polygons, circles, and composite figures;

111.34.G.8.B: find areas of sectors and arc lengths of circles using proportional reasoning;

111.34.G.8.C: derive, extend, and use the Pythagorean Theorem;

111.34.G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations;

111.34.G.9: The student analyzes properties and describes relationships in geometric figures.

111.34.G.9.A: formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

111.34.G.9.C: formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models; and

111.34.G.10: The student applies the concept of congruence to justify properties of figures and solve problems.

111.34.G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane; and

111.34.G.10.B: justify and apply triangle congruence relationships.

111.34.G.11: The student applies the concepts of similarity to justify properties of figures and solve problems.

111.34.G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

111.34.G.11.B: use ratios to solve problems involving similar figures;

111.34.G.11.C: develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods; and

111.34.G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Correlation last revised: 3/18/2014

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.