Draw a trapezoid with two sides that are the same length.

```markdown Below is one way to construct an isosceles trapezoid (a trapezoid with the two non-parallel sides equal in length): 1. **Draw the bases:** Choose a longer horizontal base \( AB \) and a shorter horizontal base \( CD \) that is parallel to \( AB \). 2. **Mark the vertices:** Let the vertices be: - \( A = (0,0) \) - \( B = (4,0) \) - \( D = (1,2) \) - \( C = (3,2) \) 3. **Connect the points:** Draw line segments to connect the points in order \( A \) to \( B \), \( B \) to \( C \), \( C \) to \( D \), and finally \( D \) to \( A \). 4. **Verify the equal sides:** Notice that the sides \( AD \) and \( BC \) are the non-parallel, slanted sides. Their lengths are equal if the following distances are the same: \[ AD = \sqrt{(1-0)^2 + (2-0)^2} = \sqrt{1+4} = \sqrt{5} \] \[ BC = \sqrt{(4-3)^2 + (0-2)^2} = \sqrt{1+4} = \sqrt{5} \] Hence, \( AD = BC = \sqrt{5} \). 5. **Graphical representation using TikZ (LaTeX):** ```latex \begin{tikzpicture}[scale=1] % Define the points \coordinate (A) at (0,0); \coordinate (B) at (4,0); \coordinate (C) at (3,2); \coordinate (D) at (1,2); % Draw the trapezoid \draw (A) -- (B) -- (C) -- (D) -- cycle; % Label the vertices \node[below left] at (A) {\(A\)}; \node[below right] at (B) {\(B\)}; \node[above right] at (C) {\(C\)}; \node[above left] at (D) {\(D\)}; % Optionally, indicate the equal non-parallel sides \node at ($(A)!0.5!(D)$) [left] {\(\sqrt{5}\)}; \node at ($(B)!0.5!(C)$) [right] {\(\sqrt{5}\)}; \end{tikzpicture} ``` The diagram above shows an isosceles trapezoid with bases \( AB \) and \( CD \) and with the non-parallel sides \( AD \) and \( BC \) equal in length. ```