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Outside the Box Geometry

# The Good

These three quizzes introduce geometry through interesting topics and challenging puzzles. This Exploration contains many of each of these types of problems:

• The Good: enjoyable problems that introduce you to essential skills

• The Badass: going beyond the essential skills to master more challenging techniques and proofs

• The Beautiful: diving deeply into areas of geometry where the elegance and beauty speaks for itself

What is the measure of the pink angle $$\angle DAE?$$

Note that $$\overline{BC}$$ and $$\overline{DE}$$ are parallel.

What is the measure of the green angle, $$\angle A?$$

Angle hunting techniques will sometimes jump out at you and seem obvious. Other times, it might not be clear how to start.

Find the measure of the red angle.

Hint: Shifting a line (without rotating it) doesn’t change the angle of its intersection with other lines.

What can we say about the base angles of any isosceles triangle?

If these three segments are connected end-to-end to form a triangle, will the triangle be acute, right, or obtuse?

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