Given that the intersection of XY and ZW is at point A
For option A :
XA = AY
This will be true only if point A is the midpoint of the segment XY, since point A is any point on the line, this conjecture is not always true.
For option B :
Take note that the two angles formed by two intersecting lines will always sum up to 180 degrees
By the definition of the acute angle, which is an angle less than 90 degrees
If XAZ is acute, The other angle is must not be acute.
Because the sum of two acute angles will not have a sum of 180 degrees.
For example 89 degrees is an acute angle and the other angle must be 180 - 89 = 91 which is not an acute angle.
So this conjecture is not always true for it may have a value of 89 degrees which is an acute, but it can also have a value of 91 degrees which is not an acute angle.
For Option C :
XY is perpendicular to ZW
This will be true only if the slope of XY and ZW is the negative inverse of each other
Since lines XY and ZW are not restricted to any slope. Therefore, this conjecture is not always true.
For option D :
X, Y, Z, and W are noncollinear
If the lines only shares at exactly one point, then the lines are noncollinear
If the lines are noncollinear, therefore the points also are noncollinear
Since XY and ZW shares at exactly one point which is the Point A, therefore the points X, Y, Z and W are noncollinear
and This conjecture is always true
The correct answer is Choice D.