INQUIRY ACTIVITY SUMMARY
45-45-90
To create a 45-45-90 triangle we must cut the square diagonally. Cutting the square diagonally will cut two of the 90 angles in half creating a 45 angle. To find the hypotenuse we must use the Pythagorean theorem. Since we know 'a' and 'b' we can plug that into the equation of a^2+b^2=c^2. Once we plug in 1 and 1 we get 2=c^2. We must get 'c' by itself and doing so by getting the square root of it canceling out the power of 2. What we do to one side we must do to the other and this gives us the 'square root of 2=c' and we now have the hypotenuse of 'square root of 2.' We use 'n' on each side because the relationship between all 45-45-90 triangles would be the same.
30-60-90
To create the special right triangle of 30-60-90 we must cut an equilateral triangle right down the center. We do this to create two triangles and it divides the top 60 angle in half and creates a 30 angle in each triangle. Doing this also makes the 90 angles at the bottom of the triangle. Put it all together and we have the 30-60-90 triangle. Since the bottom length of the triangle was 1 cutting the triangle down the middle makes it 1/2 in both triangles. To get the height of the triangle we must use the Pythagorean theorem. a=1/2 and c=1 leaving us to find 'b', the height. Since a=1/2 we will multiply all sides by 2 to get rid of the 1/2. The equation will now be 1^2+b^2=2^2. After we solve for 'b' we will get the 'square root of 3' as the height. We again use 'n' to show the relation between all 30-60-90 triangles and how they each will have the same variables such as 2n,n, and n|3.
INQUIRY ACTIVITY REFLECTION
Something I never noticed before about special right triangles is that every special right triangle will have the same relations no matter what the lengths of the triangle are.
Being able to derive these patterns myself aids in my learning because now I completely understand where the variables come from and it makes more sense of what I am doing when I am solving for problems that involve this.
