1. **Stating the problem:** We have a triangle with vertices at (0,0), (1,0), and (1,1). The sides are labeled as base $b$, height $a$, and hypotenuse $c$. The problem states the formula $a + b = c$. 2. **Understanding the triangle:** This is a right triangle with legs $a$ and $b$, and hypotenuse $c$. Normally, by the Pythagorean theorem, we have $$c^2 = a^2 + b^2.$$ However, the problem gives a different relation: $$a + b = c.$$ We will analyze this. 3. **Expressing the sides:** From the coordinates: - Base $b$ is the length from (0,0) to (1,0), so $$b = 1 - 0 = 1.$$ - Height $a$ is the length from (1,0) to (1,1), so $$a = 1 - 0 = 1.$$ 4. **Calculate $c$ using the Pythagorean theorem:** $$c = \sqrt{a^2 + b^2} = \sqrt{1^2 + 1^2} = \sqrt{2}.$$ 5. **Check the given formula $a + b = c$:** Calculate $a + b$: $$a + b = 1 + 1 = 2.$$ Compare with $c$: $$c = \sqrt{2} \approx 1.414.$$ Since $2 \neq 1.414$, the formula $a + b = c$ does not hold for this triangle. 6. **Conclusion:** The given formula $a + b = c$ is not true for the triangle with vertices (0,0), (1,0), and (1,1). The correct relation is the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}.$$