Geometry Topics:

Foundations of Geometry

This unit bundles student expectations that address the logical structure of a mathematical system. In geometry, this structure is founded on three simple concepts (point, line, and plane) that are referred to as undefined terms, and relationships between these terms are explained through additional defined terms, postulates, and theorems.

Geometry on the Coordinate Plane

This unit bundles student expectations that address connections between algebra and geometry. Coordinate systems are used for geometric explorations of distance, midpoint, slope, and parallel and perpendicular lines. Geometric conjectures are tested developing an awareness of the connections between algebra and geometry.

Properties of Lines and Transversals

This unit bundles student expectations that address the relationship between lines and their transversals, especially between parallel lines and their transversals. In this unit, logical reasoning is incorporated to formulate proofs about parallel lines.

Triangles

This unit bundles student expectations that relate to using patterns to make conjectures and then verifying whether these conjectures are true using concrete models, coordinate geometry, and formal proof. To anchor these processes in geometric content, this unit focuses on relationships between the sides and angles in triangles, and in the relationships between pairs of congruent or similar triangles.

Right Triangles

This unit bundles student expectations that address relationships in right triangles, including the Pythagorean Theorem and the trigonometric ratios.

Quadrilaterals

This unit bundles student expectations that explore the properties of quadrilaterals and the use of coordinate proofs to justify classification of quadrilaterals by analysis of the properties of their sides, angles, and diagonals.

Properties of Two-Demensional Figures

This unit bundles student expectations that address characteristics of polygons and circles. The unit addresses generating formulas for various properties of polygons and regular polygons, and applying formulas associated with properties of polygons and regular polygons in problem situations. This unit also addresses various properties of circles, including comparisons of circles and squares in Euclidean and taxicab geometries, circle vocabulary, and angle and segment relationships resulting from secant and tangent lines in circles.

Measurement of Two-Demisional Figures

This unit bundles student expectations that incorporate using multiple representations to explore and apply formulas for perimeter, area, arc length, and sector area for polygons, circles, and composite figures in problem situations, including area models. This unit also addresses solving perimeter, circumference, and area problems involving composite figures, conversions between measurement systems, and effects of dimensional change.

  Properties of Three-Demensional Figures  

This unit bundles student expectations that address characteristics of three-dimensional figures through concrete exploration of cross sections and building and exploring three-dimensional concrete models. This unit also addresses development of spatial reasoning skills by sketching orthographic and isometric views from three dimensional models and by investigating nets of three-dimensional figures.

Measurement of Three-Demensional Figures

This unit bundles student expectations that address solving measurement problems involving lateral area, surface area, and volume of three-dimensional figures using concrete models and formulas. The unit also incorporates effects of dimensional change and measurement of composite solids.