What is the measure of the angles of an equilateral triangle? Consider an equilateral triangle of side 2 and an equilateral triangle of side 3. Can they be congruent?
Sometimes
Practice makes perfect
The angles of all equilateral triangles have a measure of 60^(∘) each. Thus, the congruence depends only on the measures of the sides. Let's consider the triangles below.
The three triangles are equilateral, and since AB≅ FE we can conclude that △ ABC ≅ △ DEF. In contrast, AB≆ PQ and so △ ABC ≆ △ PQR. This tells us that the given statement is sometimes true.
Equilateral triangles aresometimescongruent.
