So the given angles are congruent. Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. +60 + 70 = +130. So [5x + 60] +  = 180. Home Geometry. Parallel Lines. Show transcribed image text. Since they are complementary there are parallel lines. D) If consecutive Interior angles are supplementary, then lines are parallel. A) If lines are parallel, then alternate Interior angles are congruent. 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 … 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. B) If alternate Interior angles are congruent, then lines are parallel. 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°). This question hasn't been answered yet Ask an expert. Previous question Next question Transcribed Image Text from this Question. Corresponding angles are congruent, alternate interior angles are congruent, same side or consecutive interior angles are supplementary, alternate exterior angles are congruent… This framework of two pairs of consecutive congruent sides, opposite angles congruent, and perpendicular diagonals is … Theorem 3-6 Consecutive Interior Angles Theorem Then x = 5. 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). Alternate Interior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. Corollary 12-A-3 There can be at most one obtuse angle in triangle. So are angles 3 and 5. Alternate interior angles are congruent. 13) Given that a//b, solve for x. Theorem 3-5 Alternate Exterior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent. C) If lines are parallel, then consecutive interior angles are supplementary. Divide both sides by 10. Consecutive interior angles are supplementary. The given angles are consecutive interior angles in parallel lines. Question: In The Figure, 21 And 22 Are Congruent Consecutive Interior Angles Alternate Interior Angles Alternate Extorior Angles. Expert Answer . 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.. Corollary 12-A-2 There can be at most one right angle in Move +130 to the right side. Then 5x = 50. So x = 5. then each pair of consecutive interior angles is supplementary.
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