Based on the diagram, decide whether each statement is true. Be prepared to share your reasoning.
The length of segment is equal to the length of segment .
Triangle is equilateral.
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2.2
Activity
Make Your Own
Use straightedge and compass moves to build your own pattern, using the circle and radius as a place to start. As you make your pattern, record each move on a separate sheet of blank paper. Use precise vocabulary so someone could make a perfect copy without seeing the original. Include instructions about how to shade or color your pattern.
2.3
Activity
Make Someone Else’s
Follow the instructions precisely to recreate your partner’s pattern.
Use the following straightedge and compass moves to create a line parallel to the given line that goes through point :
Create a line through and extending in both directions. Label this line .
Create a circle centered at with radius . This circle intersects with line in 2 places. Label the intersection point to the right of as .
Create a circle centered at with radius . This circle intersects with line at and 1 other point. Label the new intersection point as .
Create a circle centered at with a radius of length . This circle intersects with the circle centered at in 2 places. Label the intersection point to the right of as .
Using a different colored pencil, create a line through and extending in both directions.
Student Lesson Summary
We can use straightedge and compass moves to construct interesting patterns. What if someone else wants to make the same pattern? We need to communicate how to reproduce the pattern precisely. Compare these sets of instructions:
Start with a line and 2 points.
Create a line.
Create a circle.
Create a circle.
Create a circle.
Create a line.
Start with a line , point on line , and point not on line .
Create a line through and extending in both directions. Label this line .
Create a circle centered at with radius . This circle intersects with line in 2 places. Label the intersection point to the right of as .
Create a circle centered at with radius . This circle intersects with line at and 1 other point. Label the new intersection point as .
Create a circle centered at with a radius of length . This circle intersects with the circle centered at in 2 places. Label the intersection point to the right of as .
Create a line through and extending in both directions.
It is important to label points and segments, such as point or segment , to communicate precisely.
These are instructions to construct a line parallel to a given line. We say that two lines are parallel if they don’t intersect. We also say that two segments are parallel if they extend into parallel lines.
Glossary
parallel
Two lines that never intersect are called parallel. Line segments can also be parallel if they extend into parallel lines.
This figure shows two parallel line segments.
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