Rectangle Inception

They aren't congruent, they are similar! Suppose the upper-left vertex of the yellow rectangle is $A$ , the upper-right $B$ , and so on until $D$ . Now, suppose the vertex of the blue rectangle that is above $D$ is $E$ , the one to the left of $B$ is $F$ and so on until $H$ ; In $\bigtriangleup EDH$ , the upper angle is $\alpha$ , and the lower angle (not the right angle) is $\beta$ . So, $\alpha + \beta = 90°$ . We also have $\angle DHE + \angle EHG + \angle GHC = 180° \longmapsto \beta + 90° + \gamma = 180° \longmapsto \beta + \gamma = 90° \longmapsto \gamma = \alpha$ . Finally, we can conclude that $\bigtriangleup EDH$ is similar to $\bigtriangleup HCG$ . The same process aplies for the others.