Stepping Stone 6: Build It!
Learning Targets:
I can create diagrams using a straightedge.
I know to use a compass to construct a circle.
Standards Addressed:
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Vocabulary:
circle: A circle of radius r with center O is the set of all points that are a distance r units from O.
To draw a circle of radius 3 and center O, use a compass to draw all the points at a distance 3 from O.
The Right Tool
Copy the figure using only a pencil and no other tools.
Familiarize yourself with your straightedge and compass by drawing a few circles of different sizes, a few line segments of different lengths, and extending some of those line segments in both directions.
Complete these steps with a straightedge and compass:
Draw a point and label it A.
Draw a circle centered at point A with a radius of length PQ.
Mark a point on the circle and label it B.
Draw another circle centered at point B that goes through point A.
Draw a line segment between points A and B.
Discussion: Construction Moves
When doing constructions there are valid moves you can do. Using these moves guarantees a precise construction. Eyeballing where a point or segment should go means that there is no guarantee someone will be able to reproduce it accurately.
Valid Moves:
If starting from a blank space, start by marking two points.
You can create a line or line segment between two marked points.
You can create a circle centered at a marked point going through another marked point.
You can set your compass to the length between two marked points and create a circle with that radius centered at any marked point.
You can mark intersection points.
You can mark a point on a circle.
You can mark a point on a line or line segment.
Cool Down:
Here is segment AB and a point C:
Create a circle centered at C whose radius is the length of AB. Mark a point on the circle and label it D. Draw line CD and label its other intersection with the circle as point E.
