Triangle Angle Sum and Exterior Angle Properties (GeoGebra)
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Last updated almost 4 years ago
10 questions
Note from the author:
Students explore properties of triangles using GeoGebra and develop an intuitive understanding of proofs of the triangle sum theorem and external angle properties.
In this interactive lesson, you will utilize geometry software to experiment and understand two import results.
Let's start with the triangle sum property.
1
Add the three internal angles of the triangle. What do they sum to?
Add the three internal angles of the triangle. What do they sum to?
1
Now, try moving the vertices to change the shape of the triangle. What happens to the sum of the internal angles when the triangle shape changes?
Now, try moving the vertices to change the shape of the triangle. What happens to the sum of the internal angles when the triangle shape changes?
1
By moving the vertices, can you make a new triangle whose internal angle sum is different from your answer(s) above? Describe your observations about this below.
By moving the vertices, can you make a new triangle whose internal angle sum is different from your answer(s) above? Describe your observations about this below.
1
Try moving the two sliders in the top-left corner. You can also move the vertices to change the shape of the triangle. Describe your observations about the angles.
Try moving the two sliders in the top-left corner. You can also move the vertices to change the shape of the triangle. Describe your observations about the angles.
1
Select ALL true statements about the interior angles of triangles.
Select ALL true statements about the interior angles of triangles.
Next, you are going to discover the exterior angle property.
1
By the Triangle Angle Sum property, what is the value of the sum of the internal angles: \angle A + \angle B + \angle C = ?
By the Triangle Angle Sum property, what is the value of the sum of the internal angles: \angle A + \angle B + \angle C = ?
1
Suppose we label the (internal) orange angle as \angle C and the red angle as \angle C'.
Select ALL true statements.
Suppose we label the (internal) orange angle as \angle C and the red angle as \angle C'.
Select ALL true statements.
1
On the whiteboard, combine your results above and show your work to prove that the external angle of a triangle is equal to the sum of what two other angles?
On the whiteboard, combine your results above and show your work to prove that the external angle of a triangle is equal to the sum of what two other angles?
1
Select ALL true statements.
Select ALL true statements.
1
Summarize all important results you've learned in this section.
Summarize all important results you've learned in this section.