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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 enter image description here

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}

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 enter image description here

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.

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 enter image description here

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}
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user209867
user209867

Help drawing a more sophisticated right triangle with tikz or something else

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 enter image description here

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.