Question

Quadrilateral abcd has vertices a(1,0) b(5,0) c (7,2) d(3,2). use slope to prove that abcd is a parallelogram.

Answer 1

`m_{\overline{AB}}=(0-0)/(1-5)=0\\m_{\overline{CD}}=(2-2)/(3-7)=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}`

`m_{\overline{BC}}=(2-0)/(7-5)=1\\m_{\overline{AD}}=(2-0)/(3-1)=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}`

As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.