a) Choose one vertex of the triangle and its opposite side. [br][br]b) From this vertex, draw the [b]altitude[/b], the [b]median[/b], and [b]angle bisector.[/b][br][br]c) Draw the perpendicular bisector through its opposite side. [br][br]Color code your four triangle features![br][br]To construct an a[b]ltitude [/b]select your [b]perpendicular line tool [/b]and select your vertex and opposite base.[br][br]To construct a [b]median[/b] select your [b]midpoint or center tool [/b]and select the two vertices that make up your opposite base then connect your midpoint to the opposite vertex.[br][br]To construct an angle bisector select your [b]angle bisector tool [/b]and select your 3 vertices in a clockwise direction. The one vertex you choose you be in the middle. [br][br]

The point of concurrency of the perpendicular bisectors is called the ______[b][color=#0000ff]Circumcenter[/color][/b]___________

Describe what you observe about the three perpendicular bisectors in a triangle. Write and Sketch it on your paper.

This point is the center of a special circle. [br][br]Add the circle to your Geogebra sketch.[br][br][b]Steps:[/b] Find your circle toolbox, press [b]circle through point[/b] and select your circumcenter and any vertex from your triangle. [br][br][br][br]Sketch it on your paper.

Describe what you observe about the three angle bisectors in a triangle. Sketch the[br]diagram on your paper:

The point of concurrency of the angle bisectors is called the _____[b][color=#0000ff]_incenter____[/color][/b]______________.

This point is the center of a special circle. [br][br]Add the circle to your Geogebra sketch and[br]Sketch on your paper:[br][br]Steps: [br][br]1) Intersect one angle bisector and it's opposite side length[br][br]2) Find your circle toolbox, press [b]circle through point[/b] and select your incenter and the intersection you just created. [br][br][br] [br]

Task 1: Use just two perpendicular bisectors to make a circumcenter.[br]Task 2: Use just two angle bisectors to make a quick incenter.

The point of concurrency of the altitudes is called the _____________[b][color=#0000ff]orthocenter__[/color][/b]_______________ .[br] [br] [br] [br] [br][br][br] [br]

The point of concurrency of the altitudes is called the _____________[b][color=#0000ff]orthocenter__[/color][/b]_______________ .[br] [br] [br] [br] [br][br][br] [br]

The point of concurrency of the altitudes is called the _____________[b][color=#0000ff]centroid__[/color][/b]_______________ .[br] [br] [br] [br] [br][br][br] [br]

Measure the distances from the centroid to the vertex and the centroid to themidpoints. Write down any conjectures on your paper:[br][br]Steps: [br]1) Select your measure toolbox and press [b]distance or length [/b]select centroid and any vertex. Repeat for all vertices. [br][br]2. Select your measure toolbox and press [b]distance or length [/b]select centroid and midpoints. Repeat for all midpoints.[br] [br] [br][br][br] [br]

On Geogebra, highlight the three vertices of each triangle and use the polygon>tool for the six triangles created within your original triangle. Measure the areas of the six triangles created by this triangle center.Measure toolbox has a [b]Area [/b]tool [br][br]Make a conjecture about the areas of the triangles created by the centroid:[br][br] [br] [br] [br] [br][br] [br]