# Solution to the [[Six Rectangles]] Puzzle +-- {.image} [[SixRectangles.jpeg:pic]] > 6 congruent rectangles. What’s the angle? =-- ## Solution by Properties of [[Isosceles]] [[Right-angled Triangles]] and [[corresponding angles|Corresponding Angles in Parallel Lines]] +-- {.image} [[SixRectanglesLabelled.jpeg:pic]] =-- Consider the diagram labelled as above. By considering rectangle $D E F G$, the sides of the rectangle must be in the ratio $1 : 2$. Therefore, line segments $E H$ and $B D$ have the same length, as to $A B$ and $D E$. Triangle $A B D$ and $D E H$ are therefore related by a rotation of $90^\circ$, so angle $H \hat{D} A$ is $90^\circ$. This means that triangle $A D H$ is an [[isosceles]] [[right-angled triangle]]. In particular, angle $A \hat{H} D$ is $45^\circ$. Since line segments $I C$ and $H D$ are [[parallel]], this means that angle $A \hat{J} C$ is also $45^\circ$ since [[corresponding angles]] are equal. Therefore, angle $I \hat{J} A$ is $135^\circ$.