Lesson 7

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

1. Find the length of this segment to the nearest $\frac18$ of a unit.

   

   

2. Find the length of this segment to the nearest 0.1 of a unit.

   

   

3. Estimate the length of this segment to the nearest $\frac18$ of a unit.

   

   

4. Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.

1. 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.
    
2. 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.
    
3. Reflect Pentagon $C$ across line $\ell$.
   1. In the image, write the length of each side, in grid units, next to the side.
   2. In the image, write the measure of each angle in the interior.
    

Here is a grid showing triangle $ABC$ and two other triangles.

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

1. Which one? Explain how you know.

    

2. Describe a rigid transformation that takes $ABC$ to the triangle you selected.

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 $EFD$ was made by reflecting triangle $ABC$ across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.