45°-45°-90° Triangle Exploration
The 45°-45°-90° triangle is an isosceles right triangle.
Use the applet below to explore its properties.
a.
What relationship do you notice between the leg lengths of the 45°-45°-90° triangle?
b.
Use the Pythagorean Theorem to find the hypotenuse of the triangle.
How does the hypotenuse compare to the leg lengths of the 45°-45°-90° triangle?
c.
Create a ratio comparing one leg length to the other in a 45°-45°-90° degree triangle (leg/leg).
What is the value of this ratio (divide to calculate)?
Does this value change if the size of the triangle increases or decreases?
d.
Create a ratio comparing either leg length to the hypotenuse length in a 45°-45°-90° degree triangle (leg/hyp).
What is the value of this ratio (divide to convert to a decimal)?
Does this value change if the size of the triangle increases or decreases?
e.
How can you use the leg/hyp ratio to find the length of the hypotenuse if you know the length of the leg (for example, if the leg has a length of 0.75 units)?
f.
How can you use the leg/hyp ratio to find the length of the leg if you know the length of the hypotenuse (for example, if the hypotenuse has a length of 2.121 units)?