The coordinates of the endpoints of ab and cd are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which condition proves that ab//cd ?
Well, to prove that ab is parallel to cd, we must demonstrate that the slopes of both lines are equal. So, here's a joke for you: Why don't scientists trust atoms? Because they make up everything! Anyway, back to the question. We can use the formula for slope: m = (y2 - y1) / (x2 - x1). If the slope of ab is equal to the slope of cd, then they are parallel. But remember, laughter is also parallel to a good time!
Two lines are parallel if and only if their slopes are equal. Therefore, to prove that line AB is parallel to CD, we need to show that the slopes of these lines are equal.
The slope of a line passing through points A(x1, y1) and B(x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Similarly, the slope of a line passing through points C(x3, y3) and D(x4, y4) is given by:
slope = (y4 - y3) / (x4 - x3)
To prove that AB is parallel to CD, we need to show that these slopes are equal.
Therefore, the condition to prove that AB is parallel to CD is:
(y2 - y1) / (x2 - x1) = (y4 - y3) / (x4 - x3)
To determine if the line segments AB and CD are parallel (AB // CD), we need to check if their slopes are equal.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
So, the slope of AB is:
m1 = (y2 - y1) / (x2 - x1)
And the slope of CD is:
m2 = (y4 - y3) / (x4 - x3)
To prove that AB is parallel to CD, we need to show that m1 = m2.
Thus, the condition that proves that AB is parallel to CD is:
(y2 - y1) / (x2 - x1) = (y4 - y3) / (x4 - x3)
If by // you mean parallel ║ then the slopes must be the same:
(y2-y1)/(x2-x1) = (y4-y3)/(x4-x3)