Question

select the correct answer
given: t(-4,-1). r(-2,5), a(4,8), and p(8,5) are vertices of quadrilateral trap
prove: trap is a trapezoid

what is step 3 to complete the proof?
a. \\( \overline { t r } \parallel \overline { a p } \\) by the definition of parallel lines
b. \\( \overline { t r } \perp \overline { r a } \\) by the definition of perpendicular lines
c. \\( \overline { r a } \parallel \overline { p t } \\) by the definition of parallel lines
d. \\( \overline { a p } \perp \overline { r a } \\) by the definition of perpendicular lines

Explanation:

Step1: Recall the property of a trapezoid

A trapezoid has one pair of parallel sides. Parallel lines have equal slopes.

Step2: Check the slopes

From step 2, slope of \(RA=\frac{1}{2}\) and slope of \(PT = \frac{1}{2}\).

Step3: Use the definition of parallel lines

Since slope of \(RA=\) slope of \(PT\), by the definition of parallel lines (\(m_1 = m_2\) implies \(l_1\parallel l_2\)), \(\overline{RA}\parallel\overline{PT}\)

Answer:

C. \(\overline{RA}\parallel\overline{PT}\) by the definition of parallel lines