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## Classification of Triangles

Can a scalene triangle be obtuse? Is an equilateral triangle always acute?

# Equilateral Triangles

In the above diagram, $$\angle ABC=60^\circ$$ and $$\angle ACB=60^\circ.$$ If $$\lvert \overline{AB}\rvert =3,$$ what is the area of $$\triangle ABC$$?

Given two distinct points $$A$$ and $$B$$ in the plane, how many distinct points $$C$$ are there on the same plane such that $$\triangle ABC$$ is an equilateral triangle?

There are $$8$$ equilateral triangles each of which is $$4 \text{ cm}$$ on a side. All of these triangles have been made by bending copper wires. Now, you unbend the wires and try to make squares with side length $$1 \text{ cm}.$$ How many such squares can you make?

In the above diagram, the side length of equilateral triangle $$\triangle ABC$$ is $$a=3.$$ If $$D$$ is the midpoint of $$\overline{BC}$$ and $$\triangle ADE$$ is also an equilateral triangle, what is the area of $$\triangle ABE$$?

In the above diagram, the triangle is the equilateral triangle. If $$\overline{AB}=5.$$ What is the height of $$\triangle ABC$$?

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