Part 1
Copy this figure using only the Pen tool and no other tools.
[size=150]Tough isn't it? [br][br]The goal of this activity is to become a little more comfortable using the key geometry tools available in Geogebra. You’ll learn how to construct and manipulate basic geometric objects.[br][br]Let's start familiarizing ourselves with the digital straightedge and compass tools. Use the empty screen below to perform the following:[br][list=1][*][size=150]Draw a few circles of different sizes.[/size][/*][*][size=150]Draw a few line segments of different lengths.[/size][/*][*][size=150]Use the cursor to extend some of those line segments in both directions. [/size][/*][/list]Make sure to play around with every tool offered to see what it does. Once you're comfortable manipulating your drawing using these tools, please move onto the next section.[/size]
[size=150]Now, let's make a 2nd attempt at the original drawing.[br][br]Use the steps below to copy the given drawing:[br][list][*]Draw a point and label it [i]A[/i].[/*][*]Draw a circle centered at point A with a radius equal to length [i]PQ[/i].[/*][*]Mark a point on the circle and label it [i]B[/i].[/*][*]Draw another circle centered at point [i]B[/i] that goes through point [i]A[/i].[/*][*]Draw a line segment between points [i]A[/i] and [i]B[/i].[/*][/list][/size]
[size=150]Let's see what else we can make as a result of these tools.[br][br]Use the screen below (and segment AB) to complete the following instructions:[br][list=1][*]Create a circle centered at A with a radius AB.[/*][*]Create a circle centered at B with a radius BA.[/*][*]The two circles should intersect at two new points. Label the one intersection point toward the top of the page as C and the one toward the bottom as D.[/*][*]Draw a line that passes through points C and D. That line should intersect segment AB. Mark that point and label it point E.[/*][/list][/size]
Use your drawing above to answer a few questions:
What relationship does point E have to segment AB?
Draw segments connecting points A and B to point D. What type of geometric figure did you make with points ACBD? How do you know?
Draw segments connecting points A and B to point C. What is true about the triangle you just created? How do you know?
[size=150]The blue shape below is a [b]regular hexagon[/b], a six-sided figure whose sides and angles are all congruent.[br][br]The drawing next to it 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.[/size]
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?