3.4 P ROOFS WITH P ERPENDICULAR L INES OBJ: Students will be able to find the distance from a point to a line, prove theorems about perpendiculars, and 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. Perpendicular bisector: the line n with the following two properties. n PQ n passes through the midpoint M of PQ 1. Find the distance from point A to BC. 2. Find the distance from point A to BD. L INEAR P AIR P ERPENDICULAR T HEOREM If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. P ERPENDICULAR T RANSVERSAL T HEOREM In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. If hk and j h, then j k. L INES P ERPENDICULAR TO A T RANSVERSAL T HEOREM In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. If m p and n p, then mn. 3. P ROVING P ERPENDICULAR T RANSVERSAL T HEOREM 4.
