How to Construct a 45-45-90 Degree Triangle With a Compass


Hi, I'm Rachel, and today we're going to be going over how to construct a 45-45-90 right triangle with a compass. So, a 45-45-90 is an isosceles right triangle. Well, if we're making a right angle, right, a 90-degree angle, we can use the compass; we can put a point on a piece of paper and just use the ruler to draw a straight line or the part of the compass that's straight to do a straight line there. Then, take the compass, let it form a perfect 90-degree angle, right, and you do a point there. And then, you use your ruler to add or straight edge of some sort to do a straight line, like such. And that will give you a 90-degree angle. Then, you bring the compass up into the dot and you see where is 45-degree angle. Well, 45 is half of 90. So, it's going to look like, we're just drawing it without a compass, something like this. Right? That's half of a perpendicular angle, that would be right like this. So, this is 45 degrees, alright, I'll write it out here and this is also ends up being 45 degrees because that forms the perfect triangle. And just so you know for the ratio of a 45-45-90 right triangle, the sides would be x, x and x root two, in case you're going a little further in doing the sides after you've constructed it with your compass. I'm Rachel and thank you for learning with me today.

Rachel Kaplove has worked as a professional private tutor since 2005. Specializing in Math and Science, she tutors students from the second grade level to advanced high school honors levels.