Triangle Centers Activity
04_01_trianglecentersactivities
Activity 1: Place six dots anywhere on a blank page. Then connect pairs of dots.
Activity 2: Create a Scalene Triangle
Activity 2
a) Choose one vertex of the triangle and its opposite side.
b) From this vertex, draw the altitude, the median, and angle bisector.
c) Draw the perpendicular bisector through its opposite side.
Color code your four triangle features!
To construct an altitude select your perpendicular line tool and select your vertex and opposite base.
To construct a median select your midpoint or center tool and select the two vertices that make up your opposite base then connect your midpoint to the opposite vertex.
To construct an angle bisector select your angle bisector tool and select your 3 vertices in a clockwise direction. The one vertex you choose you be in the middle.
Activity 3: In a general scalene triangle, construct the three perpendicular bisectors.
Definition:
The point of concurrency of the perpendicular bisectors is called the ______Circumcenter___________
Observation 1:
Describe what you observe about the three perpendicular bisectors in a triangle. Write and Sketch it on your paper.
Observation 2:
This point is the center of a special circle.
Add the circle to your Geogebra sketch.
Steps: Find your circle toolbox, press circle through point and select your circumcenter and any vertex from your triangle.
Sketch it on your paper.
Activity 4: In a general scalene triangle, construct the three angle bisectors.
Question 1:
Describe what you observe about the three angle bisectors in a triangle. Sketch the
diagram on your paper:
Definition:
The point of concurrency of the angle bisectors is called the ______incenter__________________.
This point is the center of a special circle.
Add the circle to your Geogebra sketch and
Sketch on your paper:
Steps:
1) Intersect one angle bisector and it's opposite side length
2) Find your circle toolbox, press circle through point and select your incenter and the intersection you just created.
Activity 5: Quick circumcenters and incenters
Task 1: Use just two perpendicular bisectors to make a circumcenter.
Task 2: Use just two angle bisectors to make a quick incenter.
In a general scalene triangle, construct a quick circumcenter.
In a general scalene triangle, construct a quick incenter.
Activity 6: Construct three altitudes on a general scalene triangle. Sketch the result on your paper:
Definition:
The point of concurrency of the altitudes is called the _____________orthocenter_________________ .
Definition:
The point of concurrency of the altitudes is called the _____________orthocenter_________________ .
Activity 7: Construct three medians on a general scalene triangle. Sketch below:
Definition:
The point of concurrency of the altitudes is called the _____________centroid_________________ .
Task 1:
Measure the distances from the centroid to the vertex and the centroid to themidpoints. Write down any conjectures on your paper:
Steps:
1) Select your measure toolbox and press distance or length select centroid and any vertex. Repeat for all vertices.
2. Select your measure toolbox and press distance or length select centroid and midpoints. Repeat for all midpoints.
Task 2:
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 Area tool
Make a conjecture about the areas of the triangles created by the centroid: