Transitive property of parallel lines

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Suppose two coplanar lines are cut by a transversal. If two corresponding angles have the same measure, then the lines are parallel. If the lines are parallel, then corresponding angles have the same measure.

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Dec 21, 2020 · It is easy to check that \(S\) is reflexive, symmetric, and transitive. Let \({\cal L}\) be the set of all the (straight) lines on a plane. Define a relation \(P\) on \({\cal L}\) according to \((L_1,L_2)\in P\) if and only if \(L_1\) and \(L_2\) are parallel lines. Again, it is obvious that \(P\) is reflexive, symmetric, and transitive. • When a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal. a e b fc gd h h d b f g c a e • When a transversal intersects a pair of lines creating equal corresponding angles, the pair of lines is parallel. Need to Know • When a transversal intersects

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Theorems Involving Parallel Lines ∂ The Parallel Postulate Through a point not on a line there is exactly one parallel to the given line. ∂ Theorems on Parallel Lines, Transversals &/or Angles If two parallel lines are cut by a transversal, then any pair of the angles formed are either congruent or supplementary. Drawing a line segment in the interior of a triangle that is parallel to the base and intersects the other two sides divides the two sides into segments that are proportional. The Triangle Proportionality Theorem states: “If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.”

May 15, 2019 · Construct parallel lines. Prove theorems about parallel lines. Use the Transitive Property of Parallel Lines. Differentiating the Lesson 3.3 Angles between intersecting lines 3.4 1 day G.CO.9 G.CO.12 Find the distance from a point to a line. Construct perpendicular lines. Prove theorems about perpendicular lines. Solve real-life problems ... Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal, the following pairs of angles are congruent. • corresponding angles • alternate interior angles • alternate exterior angles Also, consecutive interior angles are supplementary.Transitive Property. If a = b and b = c, then a = c. ... a line, one and only one perpendicular can be drawn to the line. Angles: ... parallel chords intercept ...