![]() ![]() In figures, single or double arrows on a pair of lines indicate that the lines are parallel. Theorem 18: If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.īased on Postulate 11 and the theorems that follow it, all of the following conditions would be true if l // m (Figure 1).įigure 1 Two parallel lines cut by a transversal. Theorem 17: If two parallel lines are cut by a transversal, then every pair of angles formed are either equal or supplementary. The above postulate and theorems can be condensed to the following theorems: Theorem 16: If two parallel lines are cut by a transversal, then consecutive exterior angles are supplementary. Lesson Summary The famous Greek mathematician Euclid came up with the parallel postulate. Theorem 15: If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. This means interior angles are supplementary, as supplementary angles add up to 180 degrees. Theorem 14: If two parallel lines are cut by a transversal, then alternate exterior angles are equal. Theorem 13: If two parallel lines are cut by a transversal, then alternate interior angles are equal. Because m ∠1 + m ∠2 = 180 ° and m ∠5 + m ∠6 = 180° (because adjacent angles whose noncommon sides lie on a line are supplementary), and because m ∠1 = m ∠3, m∠2 = m ∠4, m ∠5 = m ∠7, and m ∠6 = m ∠8 (because vertical angles are equal), all of the following theorems can be proven as a consequence of Postulate 11. Postulate 11 can be used to derive additional theorems regarding parallel lines cut by a transversal. Summary of Coordinate Geometry Formulas.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas SWBAT: Recognize complementary and supplementary angles and prove angles congruent by.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area. ![]() Proving that Figures Are Parallelograms.Supplementary Angle Theorem: If two angles are supplementary to the same. ![]()
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