Two similar right triangles are given, with side lengths labeled. Prove: ax + by = cz

[angle A = angle X and angle C and angle Z are right angles]

Note: Write equations, use algebra. Use similar triangles, AAA similar triangles theorem, and/or Pythagorean theorem.

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The triangles are similar and we have Pythagoras:
x² + y² = z²
a² + b² = c²

Since the triangles are similar there is a number t so that:
x = ta, y = tb, z = tc...
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