Write-up #5

06/06/03

Sum it Up!

Can you create a triangle with two angles that measure 30 and 50 degrees.

Use GSP to create a triangle. Do not try to make your triangle to match mine! Label the vertices of your triangle. Label each side.

Investigate
ways to measure the angles. Highlight the angles you want to measure such as
ABC then measure. My triangle measures are:

What is the sum of the measures of the
three different angles? What does this tell you? Are all triangles 180°? If this is true, then what do you
know about the measures you are investigating?

180 – (50 + 30) = ?

Go back to your drawing and make your
angles 100°, 50°, and 30°.

How about 90
and 95 degrees?

How about 10
and 120 degrees?

How about 105
and 85 degrees?

Based on this
investigation, a triangle must have what angle sum?

Devise and
explain several different ways to illustrate the sum of

the angles in
a triangle.

Extensions

Extension-1: Given the following angle in a
triangle, what different types of triangles (acute, right, obtuse, scalene,
isosceles, equilateral) can you form?

* Exactly one right angle

* At least one acute angle

* Exactly one obtuse angle

Extension-2: How many non-overlapping
triangles will make a quadrilateral? What is the sum of the angles in a
quadrilateral?

How many
non-overlapping triangles will make a pentagon? What is the sum of the angles
in a pentagon?

Explain the
relationship between the number of sides in a convex polygon and the sum of its
angles.

Submit your
idea for an investigation to InterMath

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