A triangle can be formed when the sum of the three angle measures is equal to 180^(∘).
Practice makes perfect
We want to draw a triangle with angle measures of 45^(∘), 45^(∘), and 90^(∘). We can recall that a triangle can be formed when the sum of the angle measures is equal to 180^(∘). Let's check whether the three angle measures add up to 180^(∘).
45^(∘) + 45^(∘) + 90^(∘) = 180^(∘) ✓
The sum of the angle measures is 180^(∘). Now we can construct our triangle. We can begin by drawing an angle of 45^(∘) using a protractor. Let's call the vertex of this angle A.
Now we can draw a point B on one of the sides of the angle. Next, we can draw a 45^(∘) angle with its vertex at point B.
The third vertex of our triangle is the point of intersection between the two rays. We can denote the last vertex as point C. Finally, we can use the protractor to confirm that the measure of the remaining angle is 90^(∘). We can do so in two steps.
Place the center line of the protractor on top of BC.
Measure the angle between BC and AC.
Let's do it!
The angle formed at C has a measure of 90^(∘). In this case, we can draw a triangle with the given measures.
