Lesson 8
Moves in parallel
Unit 1
rigid transformations
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Warm Up - line moves
1. Describe a translation, rotation, or reflection that takes line l to line l’.
Then plot and label A’ and B’, the images of A and B.
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Warm Up - line moves
2. Describe a translation, rotation, or reflection that takes line l to line l’.
Then plot and label A’ and B’, the images of A and B.
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Learning Targets
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Parallel lines
What happens to parallel lines when we perform rigid transformations on them?
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Parallel lines
Use a piece of tracing paper to trace lines a and b and point K. Then use that tracing paper to draw the images of the lines under the three different transformations listed.
As you perform each transformation, think about the question:
What is the image of two parallel lines under a rigid transformation?
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Parallel lines
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Parallel lines
2. Rotate lines a and b counterclockwise 180 degrees using K as the center of rotation.
a. What do you notice about the changes that occur to lines a and b after the rotation?
b. What is the same in the original and the image?
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Parallel lines
3. Reflect lines a and b across line h.
a. What do you notice about the changes that occur to lines a and b after the reflection?
b. What is the same in the original and the image?
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Are you Ready for more?
When you rotate two parallel lines, sometimes the two original lines intersect their images and form a quadrilateral. What is the most specific thing you can say about this quadrilateral? Can it be a square? A rhombus? A rectangle that isn’t a square? Explain your reasoning.
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Let’s do some 180’s
1. The diagram shows a line with points labeled A, C, D, and B.
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Let’s do some 180’s
2. The diagram shows a line with points A and C on the line and a segment AD where D is not on the line.
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Let’s do some 180’s
3. The diagram shows two lines l and m that intersect at a point O with point A on l and point D on m.
a. Rotate the figure 180 degrees around O. Label the image of A as A’ and the image of D as D’.
b. What do you know about the relationship between the angles in the figure? Explain or show your reasoning.
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Lesson Summary
Rigid transformations have the following properties:
These facts let us make an important conclusion. If two lines intersect at a point, which we’ll call O, then a 180° rotation of the lines with center O shows that vertical angles are congruent.
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Cool Down: finding missing measurements
Points A’, B’, and C’ are the images of 180-degree rotations of A, B, and C, respectively, around point O.
Answer each question and explain your reasoning without measuring segments or angles.
1. Name a segment whose length is the same as segment AO.
2. What is the measure of angle A’OB’?
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Reflections
• Can you describe the effects of a rigid transformation on a pair of parallel lines?
• If I have a pair of vertical angles and know the angle measure of one of them, can I find the angle measure of the other?
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Practice Problems
ALL PERIODS click here to submit homework.
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Lesson Video
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