Question

problem 24
given: quadrilateral lprs,
\\( \overline { pt } \parallel \overline { rs } \\), and
\\( \overline { pt } \cong \overline { rs } \\)
prove: lprs is a trapezoid.

Explanation:

Step1: Recall the definition of a trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides.

Step2: Analyze the given information

We are given that \( \overline{PT}\parallel\overline{RS}\) and \( \overline{PT}\cong\overline{RS}\).

Step3: Use the property of parallelograms (if needed for a more detailed proof - but for the trapezoid definition)

Since a trapezoid only requires one pair of parallel sides. Here \( \overline{PT}\parallel\overline{RS}\) in quadrilateral \( LPRS\).

Answer:

Since a trapezoid is defined as a quadrilateral with one pair of parallel sides and we are given \( \overline{PT}\parallel\overline{RS}\) in quadrilateral \( LPRS\), \( LPRS\) is a trapezoid.