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# Geometry Warmups

Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.

# Angles and Shapes Warmup

Can we use each of the shapes on the left exactly once to make the shape on the right without any cutting?

(The radius of the wedges are each 1 unit, and the diameter is the circle is 2 units.)

###### Bonus: If your answer is no, can you prove that it cannot be done?

What is the maximum number of congruent equilateral triangles that all meet at a point without overlapping? (Touching at edges is still allowed.)

$$\overline{BC}$$ and $$\overline{DE}$$ are parallel lines.
The green angle is $$50 ^ \circ$$ and the purple angle is $$8 0 ^ \circ$$.

What is the red angle ( $$\angle DAE$$ ) in degrees?

The image on the left shows how hexagons could be used to cover the plane without gaps or overlaps.

Can copies of the purple region on the right be arranged to cover the plane without gaps or overlaps?

The two vertical lines are perfectly parallel. What is the sum of the three blue angles?

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