Unit 1, Lesson 7
No Bending or Stretching
Grade 8
7.1
Warm-up
For each question, the unit is represented by the large tick marks with whole numbers.
- Find the length of this segment to the nearest of a unit.
A line segment measured by a ruler above it. The ruler has units represented by large tick marks with whole numbers from 1 to 6. Each unit is evenly divided into 8 parts. The segment measures 4 and the fraction 5 over 8 units.
- Find the length of this segment to the nearest 0.1 of a unit.
A line segment measured by a ruler above it. The ruler has units represented by large tick marks with whole numbers from 1 to 5. Each unit is evenly divided into 10 parts. The segment measures 4 and the fraction 7 over 10 units.
- Estimate the length of this segment to the nearest of a unit.
A line segment measured by a ruler above it. The ruler has units represented by large tick marks with whole numbers from 1 to 5. The segment measures near 3 and the fraction 3 over 4 units.
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Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.
7.2
Activity
- Translate Polygon A so point goes to point . In the image, write the length of each side, in grid units, next to the side.
- Rotate Triangle B clockwise using as the center of rotation. In the image, write the measure of each angle in its interior.
- Reflect Pentagon C across line .
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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.
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In the image, write the measure of each angle in the interior.
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Student 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 was made by reflecting triangle across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.
| Measurements in triangle | Corresponding measurements in image |
|---|---|
| angle | angle |
| angle | angle |
| angle | angle |
Corresponding parts are the parts that match up between a figure and its scaled copy. They have the same relative position. Points, segments, angles, or distances can be corresponding.
Point in the first triangle corresponds to point in the second triangle. Segment corresponds to segment .