IM Geo.1.1 Lesson: Build It

Copy this figure using only the Pen tool and no other tools.

Familiarize yourself with your digital straightedge and compass tools by drawing a few circles of different sizes, drawing a few line segments of different lengths, and extending some of those line segments in both directions.

Copy the figure by completing these steps with the Line, Segment, and Ray tools and the Circle and Compass tools:

[list][*]Draw a point and label it [math]A[/math].[/*][*]Draw a circle centered at point [math]A[/math] with a radius equal to length [math]PQ[/math].[/*][*]Mark a point on the circle and label it [math]B[/math].[/*][*]Draw another circle centered at point [math]B[/math] that goes through point [math]A[/math].[/*][*]Draw a line segment between points [math]A[/math] and [math]B[/math].[/*][/list]

[list][*]Create a circle centered at [math]A[/math] with radius [math]AB[/math].[/*][*]Estimate the midpoint of segment [math]AB[/math], mark it with the Point on Object tool, and label it [math]C[/math].[/*][*]Create a circle centered at [math]B[/math] with radius [math]BC[/math]. Mark the 2 intersection points with the Intersection tool. Label the one toward the top of the page as [math]D[/math] and the one toward the bottom as [math]E[/math].[br][/*][*]Use the Polygon tool to connect points [math]A,D,[/math] and [math]E[/math] to make triangle [math]ADE.[/math][br][/*][/list]

Here is a hexagon with all congruent angles and all congruent sides (called a regular hexagon).

Try to draw a copy of the regular hexagon using only the pen tool. Draw your copy next to the hexagon given, and then drag the given one onto yours. What happened?

Here is a figure that shows the first few steps to constructing the regular hexagon. Use straightedge and compass moves to finish constructing the regular hexagon. Drag the given one onto yours and confirm that it fits perfectly onto itself.

How do you know each of the sides of the shape are the same length? Show or explain your reasoning.[br]

Why does the construction end up where it started? That is, how do we know the central angles go exactly 360 degrees around?