I am preparing a geometry note file for my students and I am trying to reproduce a figure I saw on Wikipedia in the proof of the Pythagorean theorem. Here is the figure
I can draw a right triangle with tikz after some trial and error, but I do not know how to color the interiors of the shapes, label the vertices, label the angles as nicely as shown in the figure below, drop a perpendicular, and mark the angles with arcs or a square for a right angle as in H and C vertices. I am a math teacher by profession and my computer and TeX proficiency are minimal. I would certainly appreciate any help with this. My aim is to create my own figures so as not to plagiarize. I thank all helpers.
Edit: here is my code for a right triangle
\begin{tikzpicture}[scale=1.25]
\coordinate (A) at (-1.5cm,-1.cm);
\coordinate (C) at (1.5cm,-1.0cm);
\coordinate (B) at (1.5cm,1.0cm);
\draw (A) -- (B) -- (C) -- (A);
\end{tikzpicture}