Last updated at Aug. 14, 2018 by Teachoo

Transcript

Ex7.4, 6 Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest. Let the given point be P and line be l We draw two line segments PN & PM such that PM ⊥ MN We have to prove: PM > PN In ΔPNM, ∠P + ∠N + ∠M = 180° ∠P + 90° + ∠M = 180° ∠P + ∠M = 180° – 90° ∠P + ∠M = 90° Since angle can’t be 0 or negative Hence, ∠ M < 90° ∠ M < ∠ N PN < PM ∴ Perpendicular line segment is the shortest Hence proved

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.