I/D2: Unit O - How can we derive the patterns for our special right triangles?

INQUIRY ACTIVITY SUMMARY

In order to get a 30-60-90 triangle, you ut an equatlateral triangle straight through the middle. Assumimg the legs in an equalateral triangle equal 1, when it is cut in half b equals 1/2. Then we must use the pythagorean theorem to solve for c. As seen above, we end up with radical 3/2 for b. Since b and c are both under 2, we multiply all sides by 2. Since not all triangles will have the side length of 1, we also mutliply everything by n.

In order to get a 45-45-90 triangle, you cut a  square diagonaly in half. In a 45-45-90 triangle, 2 sides are congruent. All sides are equal to 1. Using the pythagorean therom, seen above, c is equal to radical 2. Since not all triangles will have the side length of 1, we also mutliply everything by n.

INQUIRY ACTIVITY REFLECTION

“Something I never noticed before about special right triangles is…” I didn't know from just a square, we could get a 45-45-90 degree triangle which then we use the pythagorean theorem to figure out c.

“Being able to derive these patterns myself aids in my learning because…” if I become a cheesebucket and forget "c" then I could simply solve using the pythagorean theorem.