What can you say about the angles measures and length of the sides in an equilateral triangle?
See solution.
Practice makes perfect
For the purpose of our investigation, we will trace the larger triangle onto graph paper.
To describe a triangle we need to know the measure of its angles and length of its sides. By using a protractor we can find the angle's measure.
The angle we just measured is 60^(∘). Let's measure one more angle.
The second angle is also 60^(∘). We could find the measure of the third angle by using the protractor on the last angle. However, since the sum of a triangle's angles is 180^(∘), we can calculate the third angle with this information.
θ +60^(∘) +60^(∘)=180^(∘) ⇔ θ =60^(∘)
Therefore, in an equilateral triangle all angles are 60^(∘). Finally, we should also measure the length of the triangle's sides.
As we can see, all of the sides have the same length. We can now make two statements about equilateral triangles.
Statement 1: &All equilateral triangles have
&three angles of equal measure. [0.6em]
Statement 2: &All equilateral triangles have
&three sides of equal length.
Let's trace the smaller triangle onto the graph paper as well.
Finally, we will draw one more equilateral triangle, but with a different orientation and size.
