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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.
Solución
```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.
```
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