Question

Prove that the shortest line segment that can be drawn from a point to a given perpendicular to the given line.Please answer fast. Answer will be marked as brainliest

Answer 1

Heya User,

--> Take any point 'A' and line 'm'
--> Drop AP ⊥ line m and P' just any arbitrary point on 'm'...

--> In ΔAPP', ∠APP' = 90° ( By construction )
=> { ∠AP'P , ∠PAP' } < 90°

But, if ∠AP'P < 90° = ∠APP'
=> ∠AP'P < ∠APP'
=> AP < AP' 

--> We use the lemma:-> "In a Δ, if an angle A < B, then the opposite side a < b "

And hence, AP<AP' for all P' ∉ P .... Thus, follows our result..

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Hope you'll like the answer... :p