agra,ahmedabad,ajmer,akola,aligarh,ambala,amravati,amritsar,aurangabad,ayodhya,bangalore,bareilly,bathinda,bhagalpur,bhilai,bhiwani,bhopal,bhubaneswar,bikaner,bilaspur,bokaro,chandigarh,chennai,coimbatore,cuttack,dehradun,delhi ncr,dhanbad,dibrugarh,durgapur,faridabad,ferozpur,gandhinagar,gaya,ghaziabad,goa,gorakhpur,greater noida,gurugram,guwahati,gwalior,haldwani,haridwar,hisar,hyderabad,indore,jabalpur,jaipur,jalandhar,jammu,jamshedpur,jhansi,jodhpur,jorhat,kaithal,kanpur,karimnagar,karnal,kashipur,khammam,kharagpur,kochi,kolhapur,kolkata,kota,kottayam,kozhikode,kurnool,kurukshetra,latur,lucknow,ludhiana,madurai,mangaluru,mathura,meerut,moradabad,mumbai,muzaffarpur,mysore,nagpur,nanded,narnaul,nashik,nellore,noida,palwal,panchkula,panipat,pathankot,patiala,patna,prayagraj,puducherry,pune,raipur,rajahmundry,ranchi,rewa,rewari,rohtak,rudrapur,saharanpur,salem,secunderabad,silchar,siliguri,sirsa,solapur,sri-ganganagar,srinagar,surat,thrissur,tinsukia,tiruchirapalli,tirupati,trivandrum,udaipur,udhampur,ujjain,vadodara,vapi,varanasi,vellore,vijayawada,visakhapatnam,warangal,yamuna-nagar
Perpendicular Bisector Theorem

Perpendicular Bisector Theorem

The perpendicular of a line segment is defined as a line that splits another line segment into two halves via its midpoint at
90o. Any point on the perpendicular bisector is equidistant from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem. If a pillar stands at an angle in the middle of a bridge, all of the pillar's points will be equidistant from the bridge's endpoints.

The perpendicular bisector is a line segment that splits a line into equal size pieces by intersecting it perpendicularly. When two lines cross in such a way that they create a 90-degree angle with one another, they are called as being perpendicular to each other. A bisector, on the other hand, splits a line into two equal halves. A perpendicular bisector of a line segment AB crosses AB at 90 degrees thus divides it into two equal pieces. 

What is a Perpendicular Bisector, and how does it work?

A perpendicular bisector is a line segment that meets another line segment at a straight angle and splits it in half at its midway.

  • It bisects or splits AB into two equal parts.
  • It is perpendicular to (or makes right angles with) AB.
  • Inside the perpendicular bisector, each point is equal to point A and B.

When dealing with practical geometry, you'll frequently come across the use of perpendicular bisectors, such as when drawing an isosceles triangular or determining the center of a circle. The methods for making a perpendicular bisector of a line with a compass as well as a ruler are outlined below.

perpendicular theorem

What is the Perpendicular Bisector Theorem, and how does it work?

Any point on the perpendicular bisector is equidistant from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

perpendicular theorem

What is the Perpendicular Bisector Theorem's inverse?

The inverse of the perpendicular bisector theorem says that a point is on the perpendicular bisector of a line segment if it is equidistant from both endpoints of the line segment in the same plane.

Important Reminders

  • The SAS congruence criteria may be used to prove the perpendicular bisector theorem and its converse.
  • The perpendicular bisector theorem is utilized in the construction of various architectural entities as well as in designing structures that must be built in the center and at equal distances from both ends.

perpendicular theorem

Perpendicular Bisector Theorem is extensively discussed in NCERT Solutions Class 9 Maths Chapter 11 Constructions along with geometric tools, their characteristics, and usage.

Frequently Asked Questions

What Is a Perpendicular Bisector and what does it mean?
A perpendicular bisector is a line segment that cuts another line at a 90-degree angle. A perpendicular bisector, in other words, crosses another line at 90 degrees and splits it into equal size halves.

Is it possible for a Perpendicular Bisector to be the Median of a Triangle?
A perpendicular bisector can, in fact, be a triangle's midpoint. A median is a line segment that runs from a triangle's vertex to the middle of the side opposite that vertex. A perpendicular bisector of half is formed when the median intersects the opposing side at 90 degrees. For example, the medians of a triangle have always been perpendicular bisectors.

perpendicular theorem

What is the name of the position where a triangle's perpendicular bisectors meet?
A circumcenter of a triangular is the place where the perpendicular bisectors of a triangular intersect, and it is halfway from all the points.

What is called the Perpendicular Bisector Theorem, and how does it work?
According to the perpendicular bisector theorem, if such a point is upon a section's perpendicular bisector, it is equal from the section's ends.

Aakashians JEE Topper

Aakashians NEET UG 2023 Champions Again

Historic Results 2023 Aakashians Qualified +1 Lakh

JEE Advanced 2023

JEE Advanced 2023 Stats

JEE Advanced 2022 Topper

NEET Related Links

NEET Exam 2024

NEET 2024 Exam Dates

NEET 2024 Exam pattern

NEET 2024 Syllabus

NEET 2024 Eligibility Criteria

NEET 2024 Application

NEET UG Counselling


NEET UG Result

NEET 2024 Cut Off

Neet 2023 Toppers List Names & Rank

Neet Result 2023 Toppers list rank cut off

Neet Answer key Live Download PDF

Neet 2023 State Toppers List

JEE MAIN Related Links

JEE Main 2024

JEE Main Rank Predictor 2024

JEE Main College Predictor 2024

JEE Main 2024 Exam Dates

JEE Main 2024 Exam pattern

JEE Main 2024 Application

JEE Main 2024 Eligibility Criteria

JEE Main 2024 Syllabus

JEE Main 2024 Physics Syllabus

JEE Main 2024 Maths Syllabus

JEE Main 2024 Chemistry Syllabus

JEE Main 2024 Admit Card

JEE Main 2024 Counselling

JEE Main marks vs rank vs percentile

JEE Advanced Result 2023 live topper list

JEE Exam Preparation - How to calculate your rank jee

JEE Maths Syllabus - Important topics and weightage

JEE Advanced Related Links

JEE Advanced 2024 Exam Dates

JEE Advanced 2024 Application

JEE Advanced 2024 Eligibility Criteria

JEE Advanced 2024 Syllabus

JEE Advanced 2024 Maths Syllabus

JEE Advanced 2024 Physics Syllabus

JEE Advanced 2024 Chemistry Syllabus

JEE Advanced Exam Result

JEE Advanced Exam Dates

JEE Advanced Registration Dates

CUET Related Links

CUET 2024 Eligibility Criteria

CUET 2024 Admit Card

CUET 2024 Exam Pattern

CUET 2024 FAQs

CUET 2024 Counselling

CUET 2024 Syllabus

CUET 2024 Result

CUET 2024 Answer Key

CUET 2024 Preparation


CUET 2024 Application Form

Talk to our expert
Resend OTP Timer =
By submitting up, I agree to receive all the Whatsapp communication on my registered number and Aakash terms and conditions and privacy policy