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GeogebraExample_Ariel Cruz

Author:Ariel Cruz
Topic:Geometry

Sum of Interior Angles-Triangle

What do you think the interior angles of a triangle add up too? Does that ever change? Write your answer below.

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Here, we have triangle ABC. What happens if we move the vertices around? Go ahead and try it.

Changing Vertices

After you've moved the vertices around a bit, write down the values of their new angles below and calculate the sum.

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Sum of Interior Angles- Square

Write down the sum of the Interior Angles for a square below

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Here, we have a square. When we move the vertices around this time we might not have a Square ABCD, but let's see how the angles change. Try moving the vertices.

Once you moved the vertices, calculate the new interior angle sum. Did it change from your answer previously?

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Checking what you know!

True or False. The Interior Angle Sum changes when you move the vertices for a shape?

Select all that apply
  • A
  • B
  • C
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Checking what you know!

True or False. The sum of interior angles changes when we change the number of sides to any shape given.

Select all that apply
  • A
  • B
  • C
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Making Triangles- Try making triangle(s) inside the square by connecting the vertices of the shape using the Segment tool of Geogebra. (Hint: you shouldn't have segments overlapping)

Making Triangles

How many triangles were you able to make in the visual aid above? What do those triangles add up to in degrees? Separate your answers with semicolons.

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Making Triangles

What are your thoughts on the amount of sides of a square vs the amount of triangles you can make inside? Discuss with a partner close to you (If you get this part before your classmates, wait patiently please before moving on)

Making Triangles- Here, we have a Pentagon ABCDE. Try making triangles using the Segment tool of Geogebra to connect the vertices. (Hint: Segments shouldn't be intersecting inside the pentagon)

How many triangles were you able to make inside the pentagon?

Select all that apply
  • A
  • B
  • C
  • D
  • E
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Making Connections

The Interior Angle Sum of a Pentagon is 540 degrees. How does that sum relate to the triangles you made up above? Think about this and then discuss your thoughts with a partner (once they're ready!)

Creating a Formula!

Now, Let's try to come up with a formula for calculating the interior angles of any polygon. Write your answer below.

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Find the Sum- Use your formula from the previous question to calculate the interior sum of this shape. (You can also draw the triangles using the segment tool to visualize)

Calculations for Shape above

Write your answer in degrees below.

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EXTRA CREDIT

Do you know the name of this shape?

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