Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. C) If lines are parallel, then consecutive interior angles are supplementary. Show transcribed image text. Home Geometry. Then x = 5. If two lines in a plane are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. Consecutive interior angles are supplementary. Expert Answer . 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 consecutive interior angles are supplementary, then the lines are parallel As seen in the picture above there are consecutive interior angles which are supplementary( adds up to 180 degrees). So are angles 3 and 5. Divide both sides by 10. The given angles are consecutive interior angles in parallel lines. Theorem 3-6 Consecutive Interior Angles Theorem Corollary 12-A-3 There can be at most one obtuse angle in triangle. Alternate Interior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. Corollary 12-A-2 There can be at most one right angle in then each pair of consecutive interior angles is supplementary. Corresponding angles are congruent, alternate interior angles are congruent, same side or consecutive interior angles are supplementary, alternate exterior angles are congruent… Theorem 3-5 Alternate Exterior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent. 13) Given that a//b, solve for x. Previous question Next question Transcribed Image Text from this Question. This means, that because the diagonals intersect at a 90-degree angle, we can use our knowledge of the Pythagorean Theorem to find the missing side lengths of a kite and then, in turn, find the perimeter of this special polygon.. So the given angles are congruent. Alternate interior angles are congruent. This framework of two pairs of consecutive congruent sides, opposite angles congruent, and perpendicular diagonals is … A) If lines are parallel, then alternate Interior angles are congruent. So [5x + 60] + [70] = 180. This question hasn't been answered yet Ask an expert. Parallel Lines. Then 5x = 50. Move +130 to the right side. B) If alternate Interior angles are congruent, then lines are parallel. Question: In The Figure, 21 And 22 Are Congruent Consecutive Interior Angles Alternate Interior Angles Alternate Extorior Angles. 62 = 8 x + 6 56 = 8 x 56 — 8 = 8 x — 8 x = 7 11. m ∠ 1 = 100 °, m ∠ 2 = 80 °, m ∠ 3 = 100 °; Because the 80 ° angle is a consecutive interior angle with both ∠ 1 and ∠ 3, they are supplementary by the Consecutive Interior Angles … D) If consecutive Interior angles are supplementary, then lines are parallel. +60 + 70 = +130. Since they are complementary there are parallel lines. 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°). So x = 5.

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