Answer:
The answer is (B) ⇒ Yes. AB is parallel to CD and AD is parallel to BC
Step-by-step explanation:
There is an important fact about the parallel lines:
- Parallel lines have equal slopes
The rule of the slope of a line is:
- [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line
Let us use the fact and the rule to solve the question
∵ ABCD is a quadrilateral
∵ A = (0, 2) , B = (2, 6), C = (9, 6), D = (7, 2)
∵ The opposite sides are AB, CD and AD, BC
Find the slopes of the four sides to check the parallel sides
∵ [tex]m_{AB}=\frac{6-2}{2-0}=\frac{4}{2}=2[/tex]
∵ [tex]m_{CD}=\frac{2-6}{7-9}=\frac{-4}{-2}=2[/tex]
∵ The slope of AB = The slope of CD
∴ AB // CD
∵ [tex]m_{AD}=\frac{2-2}{7-0}=\frac{0}{7}=0[/tex]
∵ [tex]m_{BC}=\frac{6-6}{9-2}=\frac{0}{7}=0[/tex]
∵ The slope of AB = The slope of CD
∴ AD // BC
The correct answer is:
Yes. AB is parallel to CD and AD is parallel to BC ⇒ (B)
