GEOMETRY MATHEMATICS STANDARDS
Core Content #1:
List of Per- Logical arguments and
formance Ex- proofs
pectations
Distinguish between
inductive and deductive
reasoning.
A
B
C
D
E
F
2,MC
Use inductive reasoning to
make conjectures, to test the
plausibility of a geometric
statement, and to help find a
counterexample.
2,3
Use deductive reasoning to
prove that a valid geometric
statement is true.
2,3*
Write the converse, inverse,
and contrapositive of a valid
proposition and determine
their validity.
2,3,MC,SA
Identify errors or gaps in a
mathematical argument and
develop counterexamples to
refute invalid statements
about geometric relationships.
2,3,MC
Distinguish between definitions and undefined geometric terms and explain the role
of definitions, undefined
terms, postulates (axioms),
and theorems
1,MC
Core Content 3, J & K
J
K
Describe prisms, pyramids,
parallelepipeds, tetrahedra,
and regular polyhedra in
terms of their faces, edges,
vertices, and properties1,MC
Analyze cross-sections of
cubes, prisms, pyramids,
and spheres and identify the
resulting shapes.
1,2,MC
Core Content #2:
Lines and Angles
Core Content #3:
Two- and three-dimensional
figures
Know, prove, and apply
Know, explain, and apply basic
theorems about parallel and postulates and theorems about
perpendicular lines.
triangles and the special lines,
line segments, and rays
associated with a triangle.
Core Content #4:
Geometry in the coordinate
plane
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, a
line through a given point
perpendicular to a given line.
2,3,MC,CP
2,MC,SA
1,2,MC,CP
Know, prove, and apply
Determine and prove triangle
Determine the coordinates of a
theorems about angles,
congruence, triangle similarity, point that is described
including angles that arise
and other properties of
geometrically.
from parallel lines intertriangles.
sected by a transversal.
2,3,MC,SA
1,2,MC,CP
2,3,MC,CP
Explain and perform basic
Use the properties of special
Verify and apply properties of
compass and straightedge right triangles (30°–60°–90°
triangles and quadrilaterals in
constructions related to
and 45°–45°–90°) to solve
the coordinate plane.
parallel and perpendicular
problems.
lines.
1,2,MC
1,2,MC,CP
1,2,MC,SA
Describe the intersections of Know, prove, and apply the
Determine the equation of a
lines in the plane and in
Pythagorean Theorem and its
circle that is described geometspace, of lines and planes, converse.
rically in the coordinate plane &,
and of planes in space.
given equations for a circle and
a line, determine the coordi1,MC
1,2,MC,CP nates of their intersection(s). 1,2
Solve problems involving the
MC,CP
basic trigonometric ratios of
sine, cosine, and tangent.
1,2,MC,SA
Know, prove, and apply basic
theorems about parallelograms.
2,3,MC,CP
Know, prove, and apply theorems about properties of quadG
rilaterals and other polygons.
2,3,MC,CP
Know, prove, and apply basic
theorems relating circles to
H tangents, chords, radii, secants,
and inscribed angles.
2,3,MC,CP
Explain and perform constructions related to the circle.
I
1,2,MC
Core Content #5:
Geometric transformations
Core Content #6:
Additional Key Content
Core Processes:
Reasoning, Problem
Solving, Communication
Sketch results of transformations & compositions of transformations for a given two-dimensional figure on the coordinate plane, describe the rule(s)
for performing translations or for
performing reflections about the
coordinate axes or the line y = x.
2,MC
Determine and apply properties
of transformations.
Derive and apply formulas for arc
Analyze a problem situation
length and area of a sector of a circle and represent it
mathematically.
Given two congruent or similar
figures in a coordinate plane, describe a composition of translations, reflections, rotations, and
dilations that superimposes one
figure on the other.
2,MC
Describe the symmetries of twodimensional figures and describe transformations, including
reflections across a line and
rotations about a point.
2,MC,CP
Apply formulas for surface area and
volume of three-dimensional figures
to solve problems.
1,2,MC.
3,MC,SA
Analyze distance and angle measures Select and apply strategies
on a sphere and apply these measto solve problems.
urements to the geometry of the
earth.
2,MC
1
3,MC,SA
Evaluate a solution for
reasonableness, verify its
accuracy, and interpret the
solution in the context of the
original problem.
1,2,MC,CP
3,MC,SA
Predict and verify the effect that
Generalize a solution stratchanging one, two, or three linear
egy for a single problem to
dimensions has on perimeter, area,
a class of related problems,
volume, or surface area of two- and
and apply a strategy for a
three-dimensional figures.
class of related problems to
2,MC,CP solve specific problems. 3,4
Use different degrees of precision in Read and interpret diameasurement, explain the reason for grams, graphs, and text
using a certain degree of precision,
containing the symbols,
apply estimation strategies to obtain language, and conventions
reasonable measurements with apof mathematics.
propriate precision for given purpose.
2,MC,SA
2,3,SA
Solve problems involving measureSummarize mathematical
ment conversions within and between ideas with precision and
systems, including those involving
efficiency for a given
derived units, and analyze solutions in audience and purpose.
terms of reasonableness of solutions
and appropriate units
2,MC,CP
2,3
Synthesize information to
draw conclusions and evaluate the arguments andconclusions of others. 3,MC,SA
Use inductive reasoning to
make conjectures, use deductive reasoning to prove
or disprove conjectures.
4