To prove that ABCD is a trapezoid, we must prove that sides AD and BC are parallel. To do this, we determine the slopes of the lines that go through A and D and B and c.
The slope of the line that goes through A(0,0) and D(-2,4) is
The slope of the line that goes through B(2,1) and C (1,3) is
Since the two slopes are equal, the lines are parallel, meaning sides A and BC are parallel. By definition, AB is a trapezoid.
Answers & Comments
To prove that ABCD is a trapezoid, we must prove that sides AD and BC are parallel. To do this, we determine the slopes of the lines that go through A and D and B and c.
The slope of the line that goes through A(0,0) and D(-2,4) is
The slope of the line that goes through B(2,1) and C (1,3) is
Since the two slopes are equal, the lines are parallel, meaning sides A and BC are parallel. By definition, AB is a trapezoid.