Module 3: Geometric Constructions and
Trasformations
(G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.12, and G.CO.13)
Part 1: Constructions
Standards:
G.CO.12: Make formal geometric constructions, including those representing
Montana American Indians, with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and constructing a line parallel to a
given line through a point not on the line.
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Recall that the only two tools allowed in making geometric
constructions are a compass and a straightedge.
D
(Developing)
Complete one or more of the following constructions:
 Copying a segment.
 Copying an angle.
 Bisecting a segment.
 Bisecting an angle.
P
(Proficient)
Complete both of the following constructions:
 Line perpendicular to a given line through a point not on
that line.
 Line parallel to a given line through a point not on that
line.
AP
(Advanced
Proficient)
Construct a figure that requires two or more of the
aforementioned constructions. (Ex: Construct a 45 degree
angle.)
Standard:
G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Know that a regular figure is one with equal side lengths and
equal interior angle measures.
D
(Developing)
Construct a regular hexagon inscribed in a given circle.
P
(Proficient)
Construct an equilateral triangle inscribed in a given circle.
Construct a square inscribed in a given circle.
AP
(Advanced
Proficient)
Complete more complicated constructions. (Ex: A circle
through three random points, the center of a given circle, or an
octagon inscribed in a circle.
Part 2: Transformations
Standards:
G.CO.4: Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line
segments.
G.CO.2: Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in
the plane as inputs and give other points as outputs. Compare transformations
that preserve distance and angle to those that do not (e.g., translation versus
horizontal stretch).
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Identify different kinds of translations including translation,
rotation, reflection, and vertical and horizontal stretches.
D
(Developing)
Define rotations, reflections, and translations, categorizing a
given transformation as either rigid or non-ridged.
P
(Proficient)
Transform a given figure with a stretch, rotation, translation, or
reflection.
Compare two transformations according to preservation of
distance and angle.
AP
(Advanced
Proficient)
Defend whether or not the order of a given set of
transformations will affect the final figure (ie: rotate first then
translate, vs translate then rotate).
Standard:
G.CO.5: Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will carry a
given figure onto another.
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Either by hand or using computer software (ie: Geogebra or
Sketchpad) transform one figure into another using one
transformation.
D
(Developing)
Either by hand or using computer software (ie: Geogebra or
Sketchpad) transform one figure into another using two
transformations.
P
(Proficient)
Either by hand or using computer software (ie: Geogebra or
Sketchpad) transform one figure into another using three
transformations.
Given two figures, describe the transformations that will carry
onto the other.
AP
(Advanced
Proficient)
Either by hand or using computer software (ie: Geogebra or
Sketchpad) transform one figure into another using more than
three transformations.
Standard:
G.CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Recognize that rectangles, parallelograms, trapezoids, and
regular polygons can be rotated or reflected onto themselves.
D
(Developing)
Using computer software, experiment with rotations or
reflections to transform a given figure onto itself.
P
(Proficient)
Determine mathematically the angle of rotational symmetry of
a figure.
Describe how an object can be transformed using reflections
onto itself.
AP
(Advanced
Proficient)
For a given figure, determine which points can be used as a
center of rotation that give the same angle of rotational
symmetry.
Standard:
G.CO.6: Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given two figures,
use the definition of congruence in terms of rigid motions to decide if they are
congruent.
THE STUDENT WILL BE ABLE TO:
E
(Emerging)
Define rigid motions.
D
Given a figure and a rigid motion, draw the resulting figure.
(Developing)
P
(Proficient)
Given two figures, determine whether or not they are congruent
using rigid motions.
AP
(Advanced)
Create a proof that two figures are congruent using rigid motions.