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Since the lines on a notebook are parallel to each other, the transversal produces two pairs of alternate interior angles.

As an example, take a lined notebook and draw a transversal between two lines. Given two parallel lines and a transversal intersecting them, for any line parallel to the transversal, the length of the line segment between the two parallel lines will remain the same.Īlternate interior angles for parallel lines always measure the same. Two lines are said to be parallel to each other when the distance between the two lines is the same at all points. It should be noted that any transversal drawn parallel to the original transversal will produce the same set of alternate interior angles at the points of intersection, except at the point where the two non-parallel lines meet. One will not be able to figure out the angles at the second point of intersection based on this information. Since the lines are non-parallel, these angles do not share any interesting properties and measures are random depending on the geometry of the intersection, that is, if the measure of one of the eight angles at any of the points of intersection is known, one can only determine the angles at that point of intersection. ∠ P Q O \angle PQO ∠ P Q O and ∠ Q O B \angle QOB ∠ Q O B ∠ A O Q \angle AOQ ∠ A O Q and ∠ O Q R \angle OQR ∠ O Q R The following are the two pairs of alternate interior angles: This intersection produces eight angles in total, four at each point of intersection. The above figure shows the intersection of two non-parallel lines A B AB A B and P R PR P R by a transversal C D CD C D at two distinct points O and Q. The alternate interior angles lie inside the triangle. Thus, the two lines and the transversal segment between the lines together form a triangle as shown below. If the two non-parallel lines are extended to sufficient length, then they will intersect at a point. In such a case, the alternate interior angles do not have any particular properties and can be random depending on the geometry of the two lines and the transversal. When the transversal intersects two non-parallel lines, the angles formed inside the two lines on opposite sides of the transversal are called alternate interior angles.