The [b]45°-45°-90° triangle[/b] is an [b]isosceles right triangle[/b].[br]Use the applet below to explore its properties.

a.[br]What relationship do you notice between the leg lengths of the 45°-45°-90° triangle?[br][br]b.[br]Use the Pythagorean Theorem to find the hypotenuse of the triangle.[br]How does the hypotenuse compare to the leg lengths of the 45°-45°-90° triangle?[br][br]c.[br]Create a ratio comparing one leg length to the other in a 45°-45°-90° degree triangle (leg/leg).[br]What is the value of this ratio (divide to calculate)?[br]Does this value change if the size of the triangle increases or decreases?[br][br]d.[br]Create a ratio comparing either leg length to the hypotenuse length in a 45°-45°-90° degree triangle (leg/hyp).[br]What is the value of this ratio (divide to convert to a decimal)?[br]Does this value change if the size of the triangle increases or decreases?[br][br]e.[br]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)?[br][br]f.[br]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)?