You want to show that there is a unique line m perpendicular to l which passes through A. Figure 10.1 shows a line l and a point A on l.
PERPENDICULAR POSTULATE DEFINITION GEOMETRY HOW TO
Solution: Start with a game plan for how to approach the problem.Example 1: Write a formal proof for Theorem 10.1.Theorem 10.1: Given a point A on a line l, there exists a unique line m perpendicular to l which passes through A.You now have the skills to establish the uniqueness property of perpendicular lines. You learned that if you are given a point and a line, there is a unique line passing through that point that is perpendicular to the line. Remember that that the midpoint of a line segment and the angle bisector of an angle are unique. The main fact to establish about perpendicular lines has to do with uniqueness. When the lines meet to form four right angles, the lines are perpendicular. The intersecting lines either form a pair of acute angles and a pair of obtuse angles, or the intersecting lines form four right angles. If the two lines intersect at a point, the vertical angles formed are congruent. Whenever you have two lines, only one of three things can happen: Either they are the same line, they are parallel lines, or the two lines intersect at a point. I'll begin with a review of what you've learned about lines.
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