Question

the diagram shows an isosceles right triangle. follow these steps to explore the relationship between side lengths. 1. measure the length of each leg and the hypotenuse. ab = units ac = units bc = units m∠abc = 45° m∠acb = 45°

Explanation:

Step1: In isosceles right - triangle, legs are equal. Let leg length be $x$.

Let $AC = BC=x$

Step2: Use Pythagorean theorem $AB^{2}=AC^{2}+BC^{2}$. Since $AC = BC=x$, then $AB=\sqrt{x^{2}+x^{2}}=\sqrt{2x^{2}}=\sqrt{2}x$.

If we assume $x = 1$ (for simplicity of ratio), $AC = BC = 1$ unit, $AB=\sqrt{2}$ units

Answer:

$AC = 1$ unit, $BC = 1$ unit, $AB=\sqrt{2}$ units