0.3.4 No Bending or Stretching
Lesson Objectives
Required Materials
Understand what corresponding sides and
corresponding angles are for a pair of a polygons.
geometry toolkits
Identify and describe rigid transformations that
take one figure to another.
Draw the image of a figure under a rigid
transformation.
Understand that and explain why a sequence of
rigid transformations is also a rigid
transformation.
Understand and explain that distances and angle
measures are preserved under sequences of
translations, rotations, and reflections.
Setup: Measuring Segments (5 minutes)
2 minutes of quiet think time followed by whole class discussion.
Statement
Anticipated Responses
1. Determine the length of this segment to the
nearest of a unit.
1.
units
2.
units
3.
or
units
4.
units or
units
2. Determine the length of this segment to the
nearest 0.1 of a unit.
3. Estimate the length of this segment to the nearest
of a unit.
4. Estimate the length of the segment in the previous
question to the nearest 0.1 of a unit.
Setup: Sides and Angles (10 minutes)
Access to geometry toolkits, 3 mins of quiet think time, 5 mins for discussion.
Statement
1. Translate Polygon A from point
Anticipated Responses
to point
. In
the image, write the length of each side, in grid
units, next to the side.
See lesson plan
2. Rotate Triangle B 90 degrees clockwise using
the center of rotation. In the image, write the
measure of each angle in its interior.
3. Reflect Pentagon C across line .
as
a. In the image, write the length of each side, in
grid units, next to the side. You may need to
make your own ruler with the tracing paper or
a blank index card.
b. In the image, write the measure of each angle
in the interior.
Setup: Which One? (10 minutes)
Access to computers. 4 minutes quiet work time, 2 minute partner discussion, then 4 minutes for a full-class
discussion.
Statement
Here is a grid showing triangle
triangles.
Anticipated Responses
and two other
1. It’s triangle
triangle
. Triangle
is smaller than
.
2. Answers vary. Possible sequences include a
translation of to and then a 90 degree
clockwise rotation with center .
You can use a rigid transformation to take triangle
to one of the other triangles.
1. Which one? Explain how you know.
2. Describe a rigid transformation that takes
to the triangle you selected.
Setup: A Pattern Of Four Triangles (10 minutes)
Access to geometry kits. Students in groups of 3 -- 4.
Statement
Anticipated Responses
You can use rigid transformations of a figure to make
patterns. Here is a diagram built with three different
transformations of triangle
.
1. Answers vary. Sample response: I translated to
and then rotated 90 degrees clockwise with
as center.
2. Answers vary. Sample response: I translated
and then rotated 180 degrees with center
to
.
3. Answers vary. Sample response: I translated to
and then rotated 90 degrees counterclockwise
with center .
4. Yes, because rigid transformations preserve
lengths.
1. Describe a rigid transformation that takes triangle
to triangle
.
2. Describe a rigid transformation that takes triangle
to triangle
.
3. Describe a rigid transformation that takes triangle
to triangle
.
4. Diego says that segments
,
,
, and
are all the same length. Do you agree? Explain why
or why not.
Setup: Translated Trapezoid (5 minutes)
Access to geometry toolkit.
Cool-down (5 minutes)
Trapezoid
is the image of trapezoid
under a rigid transformation.
Anticipated Responses
1. Label all points on trapezoid
.
2. On both figures, label all known side lengths and
angle measures.
Lesson Summary (5 minutes)
What is a rigid transformation? Why do we call translations, rotations, and reflections rigid transformations?
What can we say about side lengths and angle measures after sequences of rigid transformations? What does it
means to be a corresponding side or corresponding angle in two figures?