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.
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.
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