Know, prove, and apply basic theorems
Know, prove, and apply theorems about
properties of quadrilaterals and other polygons.
Know, prove, and apply basic theorems
relating circles to tangents , chords, radii, secants, and inscribed
Explain and perform constructions
related to the circle.
Describe prisms, pyramids,
parallelepipeds, tetrahedra, and regular polyhedra in terms of their
faces, edges, vertices, and properties.
Analyze cross-sections of cubes,
prisms, pyramids, and spheres and identify the resulting shapes.
Determine the equation of a line in
the coordinate plane that is described geometrically, including a line
through two given points, a line through a given point parallel to a
given line, and a line through a given point perpendicular to a given
Determine the coordinates of a point
that is described geometrically.
Verify and apply
properties of triangles and quadrilaterals in the coordinate plane.
Determine the equation of a circle
that is described geometrically in the coordinate plane and, given
equations for a circle and a line, determine the coordinates of their
Sketch results of transformations and
transformations for a given two-dimensional figure on the coordinate
plane, and describe the rule (s) for performing translations or for
performing reflections about the coordinate axes or the line y = x.
Determine and apply properties of
Given two congruent or similar
figures in a coordinate plane, describe a composition of translations,
reflections, rotations, and dilations that superimposes one figure on
Describe the symmetries of
two-dimensional figures and describe transformations, including
reflections across a line and rotations about a point.
Analyze distance and angle measures
on a sphere and apply these measurements to the geometry of the earth.
Apply formulas for surface area and
volume of three-dimensional figures to solve problems.
Predict and verify the effect that
changing one, two, or three linear dimensions has on perimeter, area,
volume, or surface area of two-and three-dimensional figures.
Use different degrees of precision in
measurement, explain the reason for using a certain degree of precision,
and apply estimation strategies to obtain reasonable measurements with
appropriate precision for a given purpose.
Solve problems involving measurement
conversions within and between systems , including those involving derived units, and analyze
solutions in terms of reasonableness of solutions and appropriate units.
Analyze a problem situation and
represent it mathematically.
Select and apply strategies to solve
Evaluate a solution for
reasonableness, verify its accuracy, and interpret the solution in the
context of the original problem.
Generalize a solution strategy for a
single problem to a class of related problems, and apply a strategy for
a class of related problems to solve specific problems.
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