6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Solution: First, let “l” be a line segment and “B” be a point lying on it. A line AB perpendicular to l is now drawn. Also, let C be any other point on l. The diagram will be as follows: To prove: AB < AC Proof: In ΔABC, ∠B = 90° Now, we know that ∠A+∠B+∠C = 180° ∴ ∠A +∠C = 90° Hence, ∠C must be an acute angle which implies ∠C < ∠B So, AB < AC (As the side opposite to the larger angle is always larger)
