Two lines cut by a transversal line are parallel when the sum of the consecutive exterior angles is $\boldsymbol{180^{\circ}}$. Interior angles on the same side of the transversal are consecutive interior angles. Consecutive interior angles are the pairs of angles that are between two lines and on the same side of the line cutting through the two lines. Right. ∠1 and ∠3 > ∠ Theorem 5.1 If two lines are cut by a transversal to form a pair of congruent alternate interior angles, then the lines are parallel. Alternate and corresponding and consecutive interior and vertical angles. interior angles add up to 180. Interior Angles. Consecutive interior angles are the pairs of angles that are between two lines and on the same side of the line cutting through the two lines. Use the Consecutive Interior Angles Theorem to solve for x in the diagram. -All 4 interior angles are congruent-Diagonals are perpendicular-Interior angles add to 360-All 4 sides are congruent ... - Diagonals are congruent-Consecutive angles are supplementary-All of these are properties of rectangles. So my consecutive interior angles are gonna be this one and this one, and we know that, um Are are theories tell us that consecutive interior angles are supplementary there. Just as with exterior angles, we can have consecutive interior angles and alternate interior angles. Angles between the bounds of the two parallel lines are interior angles, again created by the transversal. So how could they ever be congruent? Which angles are congruent to angle 1 in the diagram? Student Name: Angles and Lines Module Review 29. 7 terms. Correct answers: 1 question: Consecutive interior angles are... A. Complementary B. Supplementary C. Congruent D. Colinear Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. Well, they would have to be congruent when supplementary angles are also congruent. 30. The theorem states that if the two lines are parallel, then the consecutive interior angles are supplementary to each other. Divide both sides by 10. are If you wanna have it Consecutive exterior angles are consecutive angles sharing the same outer side along the line. Consecutive Interior Angles Theorem The Theorem The Consecutive Interior Angles Theorem states that the two interior angles formed by a transversal line intersecting two parallel lines are supplementary (i.e: they sum up to 180°). In our figure a l y is the alternate interior angle for y l o making them congruent. State the theorems that support your answers. One angle is supplementary to both consecutive angles (same-side interior) One pair of opposite sides are congruent AND parallel So we’re going to put on our thinking caps, and use our detective skills, as we set out to prove (show) that a quadrilateral is a parallelogram. If two lines in a plane are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. So x = 5. Are consecutive interior angles congruent? The theorem states that if the two lines are parallel, then the consecutive interior angles are supplementary to each other. Consecutive Interior Angles. Supplementary, but they're not congruent. When the two lines intersected by the transversal are parallel corresponding angles are congruent alternate interior angles are congruent alternate exterior angles are congruent and. Math Notes. Since they are complementary there are parallel lines. 5. Consecutive interior angles are consecutive angles sharing the same inner side along the line.

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