Question

unit 1 - proving shapes

1. describe all the relationships between lines a, b, c, and d below. explain how you know this to be true (i.e. use their slopes and compare).

Explanation:

Step1: Find slope of line a

Using two - points on line a, say (0,1) and (2,2), slope $m_a=\frac{2 - 1}{2-0}=\frac{1}{2}$

Step2: Find slope of line b

Using two - points on line b, say (3,0) and (5,1), slope $m_b=\frac{1 - 0}{5 - 3}=\frac{1}{2}$

Step3: Find slope of line c

Using two - points on line c, say (-1,5) and (0,3), slope $m_c=\frac{3 - 5}{0+1}=-2$

Step4: Find slope of line d

Using two - points on line d, say (-5,0) and (-4,-2), slope $m_d=\frac{-2-0}{-4 + 5}=-2$

Step5: Analyze parallel and perpendicular relationships

Since $m_a=m_b=\frac{1}{2}$, a and b are parallel. Since $m_c=m_d=-2$, c and d are parallel. Since $m_a\times m_c=\frac{1}{2}\times(-2)=-1$, a (and b) are perpendicular to c (and d).

Answer:

Lines a and b are parallel since they have the same slope. Lines c and d are parallel since they have the same slope. Lines a (and b) are perpendicular to lines c (and d) since the product of their slopes is - 1.