If alternate interior angles are equal, then the two lines are:
Parallel
When a transversal cuts two lines, if a pair of alternate interior angles is equal, this is both a necessary and sufficient condition for the two lines to be parallel.
This is a standard converse result of the parallel lines and transversal theorem: equal alternate interior angles imply the lines never meet, i.e., they are parallel.
Similar Questions
Determine the nature of triangle formed by A(0,0), B(4,0), C(4,3).
A point P divides the line segment joining A(2, 4) and B(8, 16) internally in the ratio 1 : 2. Find the coordinates of P.
Two parallel lines are cut by a transversal. The co-interior angles are in the ratio 1 : 3. Find the smaller angle.
Important Questions from Lines
What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10?
What is the equation of the straight line cutting of an intercept 2 from the negative direction of y-axis and inclined at 30° with the positive direction of x - axis?
A straight line passes through the point (1, 1, 1) makes an angle 60° with the positive direction of z-axis, and the cosine of the angles made by it with the positive directions of the y-axis and the x-axis are in the ratio √3 : 1. What is the acute angle between the two possible positions of the line?
The graph of the in-equation 2x - 5y ≤ 5 in Cartesian plane is:
The value of k for which the pair of linear equations 4x + 6y - 1 = 0 and 2x + ky - 7 = 0 represents parallel lines is:
