[[!redirects three congruent rectangles v solutions]] # Solution to the [[Three Congruent Rectangles V]] Puzzle +-- {.image} [[ThreeCongruentRectanglesV.jpeg:pic]] > These three rectangles are congruent. What’s the angle? =-- ## Solution by Angles in an [[Isosceles]] [[Right-Angled Triangle]] +-- {.image} [[ThreeCongruentRectanglesVAnnotated.jpeg:pic]] =-- With the points labelled as above, line segments $A E$ and $E D$ are diagonals of [[congruent]] rectangles, so are of equal length. The two rectangles are at right-angles to each other, so angle $A \hat{E} D$ is $90^\circ$. Hence triangle $A E D$ is an [[isosceles]] [[right-angled triangle]] so angle $E \hat{D} A$ is $45^\circ$.