The combined area of the shaded triangles in figure 1 is equal to the combined area of the shaded triangles in figure 2. The area of the unshaded square in figure 1 can be represented by
![c^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/ojg3eiyeyhgb7bmc0ij10g1ly9bgomj27q.png)
The combined area of the two unshaded squares in Figure 2 can be represented by
![a^2+b^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/qgjx4umtc5usrvc2msm4t6s32uw5i7t0iw.png)
The areas of the equares in figure 1 and figure 2 show that
![a^2+b^2=c^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/fdnnfwrccw5g60jmi691r5gcz9ekxf8waa.png)