# Solution to the [[Three Congruent Rectangles IV]] Puzzle +-- {.image} [[ThreeCongruentRectanglesIV.png:pic]] > Three congruent rectangles. What’s the angle? =-- ## Solution by [[Symmetry]] +-- {.image} [[ThreeCongruentRectanglesIVCompleted.png:pic]] =-- Rotating the diagram by $90^\circ$ fills in the fourth rectangle. Drawing in the diagonal of the lower left rectangle thereby creates an isosceles triangle. As it is formed by the diagonals of two [[congruent]] rectangles that are at [[right-angles]] to each other, these diagonals are also at right-angles. Therefore the isosceles triangle is a [[right-angled triangle]] and so its angles are $45^\circ-45^\circ-90^\circ$. The angle is therefore $45^\circ$.