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In a coordinate plane, two nonvertical lines are parallel IFF they have the same slope. In a coordinate plane, two nonvertical lines are perpendicular IFF the product of their slopes is -1. If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.
Find the distance from a point to a line. Construct perpendicular lines. Prove theorems about perpendicular lines. Solve real-life problems involving perpendicular lines. The distance from a point to a line is the length of the perpendicular segment from the point to the line.
Prove and use theorems about perpendicular lines. • I can fi nd the distance from a point to a line. • I can construct perpendicular lines and perpendicular bisectors.
Theorem 3.11 Perpendicular Transversal Theorem In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
If two lines intersect, then they are (ALWAYS.....SOMETIMES.....NEVER) perpendicular. If two lines are coplanar, then they are (ALWAYS.....SOMETIMES.....NEVER) parallel. If two lines are cut by a transversal such that the alternate interior angles are (CONGRUENT.....COMPLEMENTARY.....SUPPLEMENTARY), then the lines are parallel.
Theorem 6: Vertical angles are equal. Def: Two lines are . perpendicular. iff they form a right angle. Theorem 7: Perpendicular lines form four right angles. Corollary to the definition of a right angle: All right angles are equal. Theorem 8: If the angles in a linear pair are equal, then their sides are perpendicular. Def: Two lines are . parallel
Prove the Perpendicular Transversal Theorem using the diagram and the Alternate Interior Angles Theorem (Theorem 3.2). The diagram shows the layout of walking paths in a town park. Determine which lines, if any, must be parallel in the diagram.
