Geometry: Transformations in the Plane Instructional Focus: Experiment ...

Geometry: Transformations in the Plane

Instructional Focus: Experiment with transformations in the plane.

CCSS and Examples Represent, describe and compare transformations (G.CO.2, G.CO.5)

A plane figure Is translated 3 units right and 2 units down. The translated figure is then reflected over the x axis. a. Draw a plane figure and represent the described transformation of the figure in the plane. b. Explain how the transformation is a function with inputs and outputs. c. Describe the relationship between the pre-image and the post-image in terms of distance and angles.

Describe the single transformation that takes the shaded triangle onto triangle . Triangle .

Describe symmetry (G.CO.3)

For each of the following shapes, describe the rotations and reflections that carry it onto itself.

4 ? Mastery Can extend thinking beyond the standard, including tasks that may involve one of the following:

? Designing ? Connecting ? Synthesizing ? Applying ? Justifying ? Critiquing ? Analyzing ? Creating ? Proving

3 ? Proficient Draw and describe transformations of reflections, rotations, translations, and combinations of these, including mapping a figure onto another.

Describe reflections, translations, and rotations as functions that take points on the plane as inputs and give other points as outputs

Compare transformations that preserve distance and angles to those that do not

Describe and illustrate rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that carry each figure onto itself.

2 - Basic Draw or describe transformations of reflections, rotations, translations, and a combination of these, including mapping a figure onto another.

Describe reflections and translations as functions that take points on the plane as inputs and give other points as outputs

Describe transformations that preserve distance and angles to those that do not

Describe or illustrate rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that carry each figure onto itself.

1 ? Below Basic Draw and describe a singular transformation of reflections and translations, including mapping a figure onto another.

Given a function rule for reflections and translations, identify the outputs

Identify transformations that preserve distance and angles to those that do not

Describe or illustrate rotations or reflections of a rectangle, parallelogram, trapezoid, or regular polygon that carry each figure onto itself.

0 ? No Evidence Little evidence of reasoning or application to

solve the problem

Does not meet the criteria in a

level 1

Develop definitions of transformations (G.CO.4 )

Is quadrilateral

A'B'C'D' a

reflection of

quadrilateral

ABCD across

the

given line? Justify your reasoning.

Develop the definition of all the terms rotations, reflections and translations in terms of:

? Angles ? Circles ? Perpendicular lines ? Parallel lines ? Line segments.

Develop the definition for 2 of the terms rotations, reflections and translations in terms of:

? Angles ? Circles ? Perpendicular lines ? Parallel lines ? Line segments.

Develop the definition for 1 of the terms rotations, reflections and translations in terms of:

? Angles ? Circles ? Perpendicular lines ? Parallel lines ? Line segments.

V2

Geometry: Transformations in the Plane

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).

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.

G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

V2

Geometry: Transformations in the Plane

Instructional Focus: Prove theorems about lines and angles

Definitions of lines and angles (G.CO.1)

Draw an example of each of the following and justify how it meets the definition of the term.

? Angles ? Circles ? Perpendicular Lines ? Parallel Lines ? Line Segments

Construction of lines and angles (G.CO.12)

How would you construct a segment perpendicular to a given segment that goes through a point on the given segment?

4 ? Mastery Can extend thinking beyond the standard, including tasks that may involve one of the following:

? Designing ? Connecting ? Synthesizing ? Applying ? Justifying ? Critiquing ? Analyzing ? Creating ? Proving

3 ? Proficient Describe the following terms using points, lines, distance and circular arcs for all of the following:

? Angles ? Circles ? Perpendicular Lines ? Parallel Lines ? Line Segments

2 - Basic Describe the following terms using points, lines, distance and circular arcs for 4 of the following:

? Angles ? Circles ? Perpendicular Lines ? Parallel Lines ? Line Segments

Use a variety of tools to perform all of the following: ? Bisect a segment ? Bisect an angle ? Construct perpendicular

lines ? Construct the

perpendicular bisector of a segment ? Construct a line parallel to a given line through a point not on the line.

Use a variety of tools to perform 4 of the following: ? Bisect a segment ? Bisect an angle ? Construct perpendicular

lines ? Construct the

perpendicular bisector of a segment ? Construct a line parallel to a given line through a point not on the line.

1 ? Below Basic Describe the following terms using points, lines, distance and circular arcs for 2 of the following:

? Angles ? Circles ? Perpendicular Lines ? Parallel Lines ? Line Segments

0 ? No Evidence Little evidence of

reasoning or application to solve the problem

Does not meet the criteria in a level 1

Use a variety of tools to perform 3 of the following: ? Bisect a segment ? Bisect an angle ? Construct perpendicular

lines ? Construct the

perpendicular bisector of a segment ? Construct a line parallel to a given line through a point not on the line.

Prove lines and angles (G.CO.9)

A carpenter is framing a wall and wants to make sure the edges of his wall are parallel. He is using a cross-brace as show in the diagram. a. What are some different ways that he could verify that the edges are parallel? b. Write a formal argument to show that these sides are parallel

Prove all of the following theorems ? Vertical angles are

congruent. ? When a transversal

crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent

Show mathematically all of the following theorems ? Vertical angles are

congruent. ? When a transversal

crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent

Identify all of the following ? Vertical angles are

congruent. ? When a transversal

crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent

V2

Geometry: Transformations in the Plane

G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G.CO.12 Make formal geometric constructions 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.

G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

V2

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