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The converse of the same-side interior angle theorem states that if a transversal intersects two lines such that a pair of same-side interior angles are supplementary, then the two lines are parallel.
11 Δεκ 2023 · The Converse of Same-Side Interior Angles Theorem Proof. Let L 1 and L 2 be two lines cut by transversal T such that ∠2 and ∠4 are supplementary, as shown in the figure. Let us prove that L 1 and L 2 are parallel. Since ∠2 and ∠4 are supplementary, then ∠2 + ∠4 = 180°.
6 Φεβ 2023 · Consecutive interior angles are pairs of angles on one side of a line—called a “transversal”—that crosses two other lines. The Consecutive Interior Angle Theorem states that when the two lines crossed by the transversal are parallel, the consecutive interior angles add up to 180°.
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.
Converse of Same Side Interior Angle Theorem: If a transversal intersects two lines in a way that a pair of the same side interior angles are supplementary, then the two lines are said to be parallel.
Consecutive Angles Theorem. Consecutive angles theorem states that if two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. From the above figure, we can write. ∠3 + ∠5 = 180 o . ∠4 + ∠6 = 180 o. Converse of Consecutive Angles Theorem
20 Σεπ 2013 · Proof of the converse of consecutive interior angles theorem. MAT.GEO.302.07 (Same Side Interior Angles - Geometry)
