# Two Isosceles Triangles +-- {.image} [[TwoIsoscelesTriangles.png:pic]] > These two isosceles triangles have the same area. What's the angle? =-- ## Solution by Properties of [[Isosceles Triangles]] and [[Equilateral Triangles]] +-- {.image} [[TwoIsoscelesTrianglesLabelled.png:pic]] =-- As both isosceles triangles have the same base and area, they must have the same height. So in the above diagram, $F B$ and $E D$ have the same length. Since triangle $F A C$ is an [[isosceles]] [[right-angled triangle]] and $B$ is the [[midpoint]] of $A C$, triangle $F B C$ is also [[isosceles]] and [[right-angled triangle|right-angled]] and so the length of $F B$ is the same as that of $B C$ and so half of that of $A C$. This means that $E D$ has half the length of $C E$, so triangle $C E D$ is half an [[equilateral triangle]]. Angle $D \hat{C} E$ is therefore $30^\circ$ so angle $E \hat{C} A$ is $150^\circ$, and finally angle $A \hat{E} C$ is $15^\circ$.