Sum of angles in a
triangle
Task
Suppose ABC is a triangle in the plane as pictured below:
Suppose M is the midpoint of AC and N is the midpoint
of BC.
a. Draw the rotation of AABC by 180 degrees about M,
labeling the image of B as B'.
b. Draw the rotation of AABC by 180 degrees about N,
labeling the image of A as A'.
c. Explain why B', C, and A' are collinear.
d. Deduce that m(ZA) + m(ZB) + m(ZC) = 180.
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