Detailed definition of alternate interior angles:

Definition of alternate interior angles is given by two alternate interior angles which come on contrary lines and on other sides of a transversal. Alternate interior angles will be equal to each other if the line are parallel. Normally this angels share side with transversal creating other side by opposite lines according to the alternate interior angles definition.

Statement of alternate interior angles theorem:

Alternate interior angles theorem typically states that, when a transversal cut two parallel lines, the resulting alternate interior angles are congruent.

How alternate interior angles are congruent:

As per the theorem a transversal cut two parallel lines . This cut generates two intersecting points on each line which have two lines passing through it that automatically creates angles. Now as both the lines are parallel they would have same alternate interior angles and thus alternate interior angles are congruent.

Few alternate interior angles examples:

Alternate interior angles examples are given below to understand them well.

1). As shown in below figure. Line 1 and Line 2 are two parallel lines. Now, as we can see another line, line 3 is cutting line 1 and line 2 at two points on both the parallel lines. As line 3 is cutting line 1 and line 2, four angles are generated shown as A,B,C and D. As we can see here angles A and D are on the opposite side of two lines and are of equal values. Same way angles B and C are on opposite side of two lines and are of equal values. Thus here both angles A and D as well as angles B and C are congruent. This states that alternate interior angles are congruent. This explains simple theorem of interior angles which are alternative, that there is always a case when two parallel lines are cut by third line they always create angles having same value on both of the lines with different sides.

alternate_interior_angles

2).Another example states that even if two lines are not parallel the interior angles created by the interaction of third line are congruent. Taking example of above figure, considering line 1 and line 2 not parallel, same theorem would be applied to angles A,B,C and D. Thus again A and D as well as B and C would be alternate interior angles and their values would be same.

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