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Classification of Triangles

Properties of 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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