Converse of Consecutive Interior Angle Theorem
According to the converse of the consecutive interior angle theorem, if a transversal intersects two lines in such a way that a pair of successive internal angles are supplementary, then the two lines are parallel.
Proof of Converse of Consecutive Interior Angle Theorem
The proof and converse of this theorem are provided below.
Using the same illustration,
∠6 + ∠4 = 180° (Consecutive Interior Angles) . . . (i)
Because ∠2 and ∠4 make a straight line,
∠2 + ∠4 = 180° (Supplementary linear pair of angles) . . . (ii)
Because the right sides of Equations (i) and (ii) are identical, we may equate the left sides of equations (i) and (ii) and express it as:
∠2 + ∠4 = ∠6 + ∠4
We obtain ∠2 = ∠6 when we solve this, which produces a similar pair in the parallel lines.
Thus, in the above figure, one set of related angles is equal, which can only happen if the two lines are parallel. This leads to the proof of the opposite of the consecutive interior angle theorem: if a transversal crosses two lines in a such that two subsequent internal angles are supplementary,
Consecutive Interior Angles
Consecutive Interior Angles are situated on the same sides of the transversal and in the case of parallel lines, consecutive interior angles add up to 180°, which implies the supplementary nature of Consecutive Interior Angles.
This article explores, almost all the possibilities related to Consecutive Interior Angles which are also called co-interior angles. This article covers a detailed expiation about Consecutive Interior Angles including, its definition, other angles related to transversal, and theorems related to Consecutive Interior Angles as well.
Table of Content
- What are Consecutive Interior Angles?
- Consecutive Interior Angles Definition
- Consecutive Interior Angles Example
- Consecutive Interior Angles for Parallel Lines
- Properties of Consecutive Interior Angles
- Consecutive Interior Angle Theorem
- Converse of Consecutive Interior Angle Theorem
- Consecutive Interior Angles of a Parallelogram
- Consecutive Interior Angles – FAQs
- Define Consecutive Interior Angles.