Consecutive Interior Angles Converse If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. This can be proved by showing that the angles inside the two lines and on the Same side of the transversal are supplementary (add to 180 degrees) than you can conclude the lines are parallel. Alternate Interior Angles Needs No Description Same Thing As Alternate Exterio Alternate Interior Angles Interior And Exterior Angles Alternate Exterior Angles . Determine which lines, if any, can be proved parallel given the angle relationship. <3, <5 Postulate 15- when two parallel lines are cut by a transversal line, the pairs of corresponding angles become congruentTerms. If a pair of consecutive interior angles formed by a transversal are supplementary angles, the lines crossed are parallel lines. Rule Converse Consecutive Interior Angles Theorem If a pair of consecutive interior angles formed by a transversal are supplementary angles, the lines crossed are parallel lines. r || s by the Converse of Consecutive Interior Angles Theorem. We say this is a converse theorem, because it is similar to an inverse function. Converse of … consecutive interior angles are supplementary. Thus the converse of alternate interior angles theorem is proved. Consecutive Interior Angles Converse If transversal forms interior angles that are supplementary angles by cutting two line, then the lines are parallel. c and e are Consecutive Interior Angles. Consecutive Interior Angles Converse. In this converse we need to prove that lines AB and CD are parallel. To help you remember: the angle pairs are Consecutive (they follow each other), and they are on the Interior of the two crossed lines.. CONSECUTIVE INTERIOR ANGLES CONVERSE PROOF. This theorem states that if two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are said to be parallel. Let us prove that l 1 and l 2 are parallel. (Click on "Consecutive Interior Angles" to have them highlighted for you.) Rule Converse Consecutive Interior Angles Theorem If a pair of consecutive interior angles formed by a transversal are supplementary angles, the lines crossed are parallel lines. Consecutive Interior Angles Converse; Last Page; Theorem 6.4-6.5; Theorem 6.6-6.7; Theorem 3.6 If two lines are cut by transversal so the consecutive interior angles are supplementry, then the lines are parallel. The consecutive interior angles converse states that If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Converse of the Consecutive Interior Angles Theorem 3-4 . The two angles in the figure sum to so lines and are in fact parallel. ANSWER: u || v; Consecutive Interior Angles Converse 13. We explain Consecutive-Interior Angles Converse with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Consider the line AB ∠(c) + ∠(d) = 180° ∠(c) + ∠(d) = ∠(c) + ∠(f) ∠(d) = ∠(f)Since, ∠(d) and ∠(f) are alternate angle and are equal.Therefore, AB is parallel to CD. If a transversal intersects two lines in such a way that a pair of consecutive interior angle are supplementary, then the two lines are parallel. The theorem is named the Converse Consecutive Interior Angles Theorem because the same thing holds true but in opposite order. Theory and exercises for math. Consecutive exterior angles; Consecutive interior angles: These angles lie on the inside of the two parallel lines and on the same side of the transversal. If you can show that angles inside the two lines and on the SAME side of the transversal are supplementary (add to 180 degrees) than you can conclude the lines are parallel. Use this section to learn this theorem in a simple way. Theorem 3-11 If two different lines are parallel to a third line, then they are parallel to each other. This lesson will demonstrate how to prove lines parallel with the converse of the consecutive-interior angles theorem. 37, p. 168 If Z3 and L'5 are supplementary, thenj Il k. I: EXAMPLE 1 Apply the Corresponding Angles Converse ALGEBRA Find the value of x that makes m n. (3x + 3.7) 4. yes; Consecutive Interior Angles Converse (Thm. Theorem 3 6 consecutive interior angles converse. Converse Consecutive Interior Angles Theorem. For example, in the figure above the lines A ∣∣ BA\ ||\ BA ∣∣ B because α\alphaα and β\betaβ is a pair of consecutive interior angles with an angle sum of 180∘,180^\circ,180∘, which makes them supplementary angles. SOLUTION: Vertical angles are congruent. < 13 ≅ <15 f. If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel. Using the converse of the Consecutive Interior Angles Theorem, you should be able to identify that if the two angles in the figure are supplementary, then lines and are parallel. Check all that apply Linear pairs that add up to 180 degrees Proof: Ex. c and e are Consecutive Interior Angles. If transversal forms interior angles that are supplementary angles by cutting two line, then the lines are parallel. The pair of consecutive interior angles for the two sections in the above figure can be named as \( (\angle \text A, \angle \text B) \) and \( (\angle \text E, \angle \text F) \). We will now show that the opposite is also true. Angle Relationship Parallel Lines Converse a. 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