Lesson 6No Bending or Stretching

Learning Goal

Let’s compare measurements before and after translations, rotations, and reflections.

Learning Targets

I can describe the effects of a rigid transformation on the lengths and angles in a polygon.

Lesson Terms

corresponding
rigid transformation

Warm Up: Measuring Segments

For each question, the unit is represented by the large tick marks with whole numbers.

Find the length of this segment to the nearest $\frac{1}{8}$ of a unit.
Find the length of this segment to the nearest 0.1 of a unit.
Estimate the length of this segment to the nearest $\frac{1}{8}$ of a unit.
Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.

Activity 1: Sides and Angles

Translate Polygon $A$ so point $P$ goes to point $P^{'}$ . In the image, write in the length of each side, in grid units, next to the side using the draw tool.
open applet in presentation mode
Rotate Triangle $B$ $90$ degrees clockwise using $R$ as the center of rotation. In the image, write the measure of each angle in its interior using the draw tool.
open applet in presentation mode
Reflect Pentagon $C$ across line $ℓ$ .
- In the image, write the length of each side, in grid units, next to the side.
- In the image, write the measure of each angle in the interior.
open applet in presentation mode

Print Version

Translate Polygon $A$ so point $P$ goes to point $Q$ . In the image, write the length of each side, in grid units, next to the side.
Rotate Triangle $B$ $90$ degrees clockwise using $R$ as the center of rotation. In the image, write the measure of each angle in its interior.
Reflect Pentagon $C$ across line $ℓ$ .
- 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 tracing paper or a blank index card.
- In the image, write the measure of each angle in the interior.

Activity 2: Which One?

Here is a grid showing triangle $A B C$ and two other triangles.

open applet in presentation mode

You can use a rigid transformation to take triangle $A B C$ to one of the other triangles.

Which one? Explain how you know.
Describe a rigid transformation that takes $A B C$ to the triangle you selected.

Print Version

Here is a grid showing triangle $A B C$ and two other triangles.

A grid with three triangles - ABC, BDE, and CGF

You can use a rigid transformation to take triangle $A B C$ to one of the other triangles.

Which one? Explain how you know.
Describe a rigid transformation that takes $A B C$ to the triangle you selected.

Lesson Summary

The transformations we’ve learned about so far, translations, rotations, reflections, and sequences of these motions, are all examples of rigid transformations. A rigid transformation is a move that doesn’t change measurements on any figure.

Earlier, we learned that a figure and its image have corresponding points. With a rigid transformation, figures like polygons also have corresponding sides and corresponding angles. These corresponding parts have the same measurements.

For example, triangle $E F D$ was made by reflecting triangle $A B C$ across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.

Triangle A, B, C and its image after reflection and translation.

measurements in triangle $A B C$	corresponding measurements in image $E F D$
$A B = 2.24$	$E F = 2.24$
$B C = 2.83$	$F D = 2.83$
$C A = 3.00$	$D E = 3.00$
$m ∠ A B C = {71.6}^{\circ}$	$m ∠ E F D = {71.6}^{\circ}$
$m ∠ B C A = {45.0}^{\circ}$	$m ∠ F D E = {45.0}^{\circ}$
$m ∠ C A B = {63.4}^{\circ}$	$m ∠ D E F = {63.4}^{\circ}$

Lesson 6No Bending or Stretching

Learning Goal

Learning Targets

Lesson Terms

Warm Up: Measuring Segments

Problem 1

Activity 1: Sides and Angles

Problem 1

Activity 2: Which One?

Problem 1

Lesson Summary