Base φ has Fibonacci-like properties. φ² = φ¹ + φ⁰, φ⁷ = φ⁶ + φ⁵, and so on. I'm not sure of the practical use of this, but it's pretty neat. No answer needed!

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?