Unit 1, Lesson 9
Composing Figures
Accelerated 7
9.1
Warm-up
Notice and Wonder: Angles of an Isosceles Triangle
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here is triangle
Draw midpoint
Rotate triangle
What kind of quadrilateral is
The picture shows 3 triangles. Triangle 2 and Triangle 3 are images of Triangle 1 under rigid transformations.
Describe a rigid transformation that takes Triangle 1 to Triangle 2. What points in Triangle 2 correspond to points
Describe a rigid transformation that takes Triangle 1 to Triangle 3. What points in Triangle 3 correspond to points
Find two pairs of line segments in the diagram that are the same length, and explain how you know they are the same length.
Find two pairs of angles in the diagram that have the same measure, and explain how you know they have the same measure.
Here is isosceles triangle
Reflect triangle
What is the measure of angle
What is the measure of angle
Reflect triangle
How long is segment
What is the measure of angle
If you continue to reflect each new triangle this way to make a pattern, what will the pattern look like?
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
Because points
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.