In trapezoid $A B C D$ the base $A D=2$, the base $B C=1$. The lateral sides $A B=C D=1$. Find the diagonals of the trapezoid.

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Through vertex $C$, draw a line parallel to $A B$.

## Solution

Through vertex $C$, we draw a line parallel to $A B$, intersecting the base $A D$ at point $M$. Note that the median $A M$ of triangle $A C D$ is equal to half the side $A D$. Therefore, $\angle A C D=90^{\circ}$. In the same triangle, the leg $C D$ is equal to half the hypotenuse. Thus, $A C=C D \sqrt{3}$.

## Answer

![](https://cdn.mathpix.com/cropped/2024_05_06_3ae27f1f0c68451d31a7g-43.jpg?height=89&width=109&top_left_y=2392&top_left_x=11)