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

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UpStudy AI · Accepted Answer

```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.
```
To draw an isosceles trapezoid with two equal non-parallel sides, follow these steps: 1. **Draw the Bases:** - Draw a longer horizontal base $$ AB $$. - Draw a shorter horizontal base $$ CD $$ parallel to $$ AB $$. 2. **Mark the Vertices:** - Let $$ A = (0,0) $$, $$ B = (4,0) $$, $$ D = (1,2) $$, and $$ C = (3,2) $$. 3. **Connect the Points:** - Draw lines $$ AB $$, $$ BC $$, $$ CD $$, and $$ DA $$ to form the trapezoid. 4. **Verify Equal Sides:** - Calculate the lengths of $$ AD $$ and $$ BC $$: $$ AD = \sqrt{(1-0)^2 + (2-0)^2} = \sqrt{1+4} = \sqrt{5} $$ $$ BC = \sqrt{(4-3)^2 + (0-2)^2} = \sqrt{1+4} = \sqrt{5} $$ - Both $$ AD $$ and $$ BC $$ are equal, confirming the trapezoid is isosceles. 5. **Optional:** - Use TikZ in LaTeX to create a graphical representation of the trapezoid. This results in an isosceles trapezoid where the non-parallel sides are equal in length.

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

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