Question

part a
the pythagorean theorem states that for any given right triangle, $a^{2}+b^{2}=c^{2}$. using the pythagorean theorem, what should be the relationship between the areas of the three squares?

Explanation:

Step1: Recall square - area formula

Area of square with side length $s$ is $A = s^{2}$. Let sides of right - triangle be $a$, $b$, $c$. Areas of squares on sides $a$, $b$, $c$ are $A_1=a^{2}$, $A_2 = b^{2}$, $A_3=c^{2}$.

Step2: Apply Pythagorean theorem

Since $a^{2}+b^{2}=c^{2}$, then $A_1 + A_2=A_3$.

Answer:

The sum of the areas of the two smaller squares is equal to the area of the largest square.