AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

State true or false.

Of all line segments that can be drawn to a given line, from a point, not lying on it, the perpendicular line segment is the shortest.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

To check if the perpendicular line segment is the shortest.
Draw a straight line,

l

and

A

is a point that is not lying on

l

A B

is perpendicular to line

l

.
And

C

is the point on

l

as shown in the figure given below.
Question Image

Consider

Δ A B C

, since sum of the angles of a triangle is

180 °

∠ A + ∠ B + ∠ C = 180 °

Substitute the known values,

∠ A + 90 ° + ∠ C = 180 °

∠ A + ∠ C = 180 ° − 90 °

∠ A + ∠ C = 90 °

Consider that an angle cannot be

0

or negative.
Therefore,

∠ C < 90 °

.
And

∠ C < ∠ B

A B < A C

. (The side

A C

opposite to the greater angle is longer)
As

C

is that point which can lie anywhere on the line

l

.
Therefore,

A B

is the shortest line segment drawn from

A

to the line,

l

.
Hence the statement is true.
Hence option 1 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!