Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Consecutive Interior Angles Theorem Consecutive Interior Angles When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.
Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. Definition of linear pair. Supplement Postulate.
When a transversal intersects two parallel lines, the alternate interior angles formed are always equal. When a transversal intersects two parallel lines, the alternate exterior angles formed are always equal. When a transversal intersects two parallel lines, the consecutive interior angles are always supplementary. The relation between the consecutive interior angles is determined by the consecutive interior angle theorem. We know that the two lines are parallel, thus we have:.
The converse of consecutive interior angle theorem states that if a transversal intersects two lines such that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
The proof of this theorem and its converse is shown below. Thus, a pair of corresponding angles are equal, which can only happen if the two lines are parallel. Hence, the converse of consecutive interior angle theorem is proved. Check out these interesting articles to know more about consecutive interior angles and their related topics.
Therefore the lines 'l' and 'm' are NOT parallel. Example 2: Using the consecutive interior angles theorem, find the value of angle 'x' if line 1 and line 2 are parallel?
Example 3: In the following figure, line 'l' is parallel to the line 'm'. Find the consecutive angles labeled in the following figure. By the consecutive interior angle theorem, these angles are supplementary. Consecutive interior angles are formed when a transversal passes through a pair of parallel lines or non-parallel lines.
They are formed on the interior sides of the two crossed lines at the point where the transversal intersects the two lines. If the lines that the transversal crosses are parallel, then, the pair of consecutive interior angles are supplementary. Consecutive interior angles are the angles that are formed on the internal side of a transversal when it crosses two lines that are parallel. When the transversal passes through two parallel lines, then the consecutive interior angles that are formed are supplementary.
The consecutive interior angles theorem states that the transversal passing through two parallel lines makes two pairs of consecutive interior angles that are supplementary. The converse of the consecutive interior angles theorem states that if a transversal intersects two lines such that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
Show Solution Check. Related Lessons. Parallel Lines as Translates of One Another. Find and Use Corresponding Angles. View All Related Lessons. Caroline K. Consecutive interior angles: Consecutive interior angles are interior angles that lie on the same side of the transversal. Created on Sketch. Let's practice identifying consecutive interior angles! Which of the following are interior angles? Consecutive exterior angles: Consecutive exterior angles are exterior angles that lie on the same side of the transversal.
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