Unit 1, Lesson 10
Composing Figures
Grade 8
10.1
Warm-up
What do you notice? What do you wonder?
10.2
Activity
Here is triangle .
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Draw midpoint of side .
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Rotate triangle using center to form a new triangle. Draw this triangle, and label the new point .
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What kind of quadrilateral is ? Explain how you know.
10.3
Activity
The picture shows 3 triangles. Triangle 2 and Triangle 3 are images of Triangle 1 under rigid transformations.
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Describe a rigid transformation that takes Triangle 1 to Triangle 2. What points in Triangle 2 correspond to points , , and in the original triangle?
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Describe a rigid transformation that takes Triangle 1 to Triangle 3. What points in Triangle 3 correspond to points , , and in the original triangle?
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Find two pairs of line segments in the diagram that are the same length, and explain how you know they are the same length.
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Find two pairs of angles in the diagram that have the same measure, and explain how you know they have the same measure.
10.4
Activity
Here is isosceles triangle . Its sides and have equal lengths. Angle is . The length of is 5 units.
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Reflect triangle across segment . Label the new vertex .
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What is the measure of angle ?
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What is the measure of angle ?
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Reflect triangle across segment . Label the point that corresponds to as .
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How long is segment ? How do you know?
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What is the measure of angle ?
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If you continue to reflect each new triangle this way to make a pattern, what will the pattern look like?
Student Lesson Summary
Earlier, we learned that if we apply a sequence of rigid transformations to a figure, then corresponding sides have equal length and corresponding angles have equal measure. These facts let us figure out things without having to measure them!
For example, here is triangle .
We can reflect triangle across side to form a new triangle:
Because points and are on the line of reflection, they do not move. So the image of triangle is . We also know that:
- Angle measures because it is the image of angle .
- Segment has the same length as segment .
When we construct figures using copies of a figure made with rigid transformations, we know that the measures of the images of segments and angles will be equal to the measures of the original segments and angles.
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