Classification of Triangles

Properties of Equilateral Triangles


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

Given two distinct points AA and BB in the plane, how many distinct points CC are there on the same plane such that ABC\triangle ABC is an equilateral triangle?

There are 88 equilateral triangles each of which is 4 cm4 \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 cm.1 \text{ cm}. How many such squares can you make?

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

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


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