# Solution to the [[Two Rectangles]] Puzzle +-- {.image} [[TwoRectangles.jpeg:pic]] > How would you find the angle between the diagonals of these two rectangles? =-- ## Solution by [[Congruent|Congruent Shapes]] and Angles in [[Isosceles]] [[Right-Angled Triangles]] +-- {.image} [[TwoRectanglesAnnotated.jpeg:pic]] =-- In the above diagram, point $E$ is so that $A C E G$ is a [[rectangle]]. Therefore, $E D$ has length $5 - 3 = 2$ and $E G$ has length $1 + 2 = 3$. Therefore, rectangle $G H D E$ is [[congruent]] to rectangle $D I B C$ but rotated by $90^\circ$. Hence angle $G \hat{D} B$ is $90^\circ$, and line segments $G D$ and $B D$ have the same length. Therefore, triangle $G D B$ is an [[isosceles]] [[right-angled triangle]]. Hence angle $D \hat{B} G$ is $45^\circ$.