Define consecutive interior angles:
Consider two lines intercepted by a transversal as shown in the figure below:
In the above figure, two lines l and m are intercepted by a transversal n. That leads to the formation of four interior angles named a, b, c and d. Of these four angles, angles a and b are called consecutive interior angles and the angles c and d are another pair of consecutive interior angles. In other words, the angles formed on the same side of the transversal are called consecutive interior angles.
Consecutive interior angles examples:
In the above figure following are pairs of consecutive interior angles:
1 – 4, 2 – 3 , 5 – 6, 7 – 8, 9 – 11, 10 – 12, 13 – 16, 14 – 17 etc.
Theorem for consecutive interior angles for parallel lines:
If a pair of parallel lines are intercepted by a transversal, then each of the pairs of consecutive interior angles is supplementary.
See the following figure:
In the above figure, we have two lines l and m that are parallel to each other. The pair of consecutive interior angles marked in blue in this case would add up to 180 degrees or the angles are said to be supplementary to each other.
Consecutive interior angles converse theorem:
If two lines are intercepted by a transversal such that each pair of consecutive interior angles is supplementary ( that means that each pair of alternate interior angle measures add up to 180 degrees) then the lines have to be parallel to each other. See figure below to understand that better:
In the above figure, one of the pair of consecutive interior angles is
Consider two lines intercepted by a transversal as shown in the figure below:
In the above figure, two lines l and m are intercepted by a transversal n. That leads to the formation of four interior angles named a, b, c and d. Of these four angles, angles a and b are called consecutive interior angles and the angles c and d are another pair of consecutive interior angles. In other words, the angles formed on the same side of the transversal are called consecutive interior angles.
Consecutive interior angles examples:
In the above figure following are pairs of consecutive interior angles:
1 – 4, 2 – 3 , 5 – 6, 7 – 8, 9 – 11, 10 – 12, 13 – 16, 14 – 17 etc.
Theorem for consecutive interior angles for parallel lines:
If a pair of parallel lines are intercepted by a transversal, then each of the pairs of consecutive interior angles is supplementary.
See the following figure:
In the above figure, we have two lines l and m that are parallel to each other. The pair of consecutive interior angles marked in blue in this case would add up to 180 degrees or the angles are said to be supplementary to each other.
Consecutive interior angles converse theorem:
If two lines are intercepted by a transversal such that each pair of consecutive interior angles is supplementary ( that means that each pair of alternate interior angle measures add up to 180 degrees) then the lines have to be parallel to each other. See figure below to understand that better:
In the above figure, one of the pair of consecutive interior angles is
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