Nebraska Geometry Math Standards

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MA 11.3 Geometry

• MA 11.3.1 Students will identify and describe geometric characteristics and create two- and three-dimensional shapes.
  • MA 11.3.1.a Know and use precise definitions of ray, line segment, angle, perpendicular lines, parallel lines, and congruence based on the undefined terms of geometry: point, line and plane.
  • MA 11.3.1.b Prove geometric theorems about angles, triangles, congruent triangles, similar triangles, parallel lines with transversals, and quadrilaterals using deductive reasoning.
  • MA 11.3.1.c Apply geometric properties to solve problems involving similar triangles, congruent triangles, quadrilaterals, and other polygons.
  • MA 11.3.1.d Identify and apply right triangle relationships including sine, cosine, tangent, special right triangles, and the converse of the Pythagorean Theorem.
  • MA 11.3.1.e Create geometric models to visualize, describe, and solve problems using similar triangles, right triangles, and trigonometry.
  • MA 11.3.1.f Know and use precise definitions and terminology of circles, including central angle, inscribed angle, arc, intercepted arc, chord, secant, and tangent.
  • MA 11.3.1.g Apply the properties of central angles, inscribed angles, angles formed by intersecting chords, and angles formed by secants and/or tangents to find the measures of angles related to the circle.
  • MA 11.3.1.h Sketch, draw, and construct appropriate representations of geometric objects using a variety of tools and methods which may include ruler/straight edge, protractor, compass, reflective devices, paper folding, or dynamic geometric software.
  • Checkpoint opportunity
• MA 11.3.2 Students will determine location, orientation, and relationships on the coordinate plane.
  • MA 11.3.2.a Derive and apply the midpoint formula.
  • MA 11.3.2.b Use coordinate geometry to analyze linear relationships to determine if lines are parallel or perpendicular.
  • MA 11.3.2.c Given a line, write the equation of a line that is parallel or perpendicular to it.
  • MA 11.3.2.d Derive and apply the distance formula.
  • MA 11.3.2.e Use coordinate geometry to prove triangles are right, acute, obtuse, isosceles, equilateral, or scalene.
  • MA 11.3.2.f Use coordinate geometry to prove quadrilaterals are trapezoids, isosceles trapezoids, parallelograms, rectangles, rhombi, kites, or squares.
  • MA 11.3.2.g Perform and describe positions and orientation of shapes under a single translation using algebraic notation on a coordinate plane.
  • MA 11.3.2.h Perform and describe positions and orientation of shapes under a rotation about the origin in multiples of 90 degrees using algebraic notation on a coordinate plane.
  • MA 11.3.2.i Perform and describe positions and orientation of shapes under a reflection across a line using algebraic notation on a coordinate plane.
  • MA 11.3.2.j Perform and describe positions and orientation of shapes under a single dilation on a coordinate plane.
  • MA 11.3.2.k Derive the equation of a circle given the radius and the center.
  • Checkpoint opportunity
• MA 11.3.3 Students will perform and compare measurements and apply formulas.
  • MA 11.3.3.a Convert between various units of length, area, and volume (e.g., such as square feet to square yards).
  • MA 11.3.3.b Convert between metric and standard units of measurement.
  • MA 11.3.3.c Apply the effect of a scale factor to determine the length, area, and volume of similar two- and three-dimensional shapes and solids.
  • MA 11.3.3.d Find arc length and area of sectors of a circle.
  • MA 11.3.3.e Determine surface area and volume of spheres, cones, pyramids, and prisms using formulas and appropriate units.
  • Checkpoint opportunity.

MA 11.4 Data

• MA 11.4.3 Students will interpret and apply concepts of probability.
  • MA 11.4.3.a Construct sample spaces and probability distributions.
  • MA 11.4.3.b Use appropriate counting techniques to determine the probability of an event.
  • MA 11.4.3.c Determine if events are mutually exclusive and calculate their probabilities in either case.
  • Checkpoint opportunity