# Solution to the Three Congruent Triangles II Puzzle +-- {.image} [[ThreeCongruentTrianglesII.png:pic]] > These triangles are congruent. What’s the angle? =-- ## Solution by [[Angles on a Straight Line]], [[Isosceles Triangle]], and [[Angles in a Triangle]] +-- {.image} [[ThreeCongruentTrianglesIILabelled.png:pic]] =-- With the points labelled as above, the congruency of the triangles is so that $A F B$ rotates to $E B D$ which then reflects to $C B D$. Therefore, the angles at $B$ are all the same and so since [[angles on a straight line]] add up to $180^\circ$ each must be $60^\circ$. This means that angle $C \hat{B} E$ is $120^\circ$. Since $B E$ and $B C$ are the same length, triangle $E B C$ is [[isosceles]] and so since [[angles in a triangle]] add up to $180^\circ$, angle $E \hat{C} B$ is $30^\circ$.