Class 9 Exam  >  Class 9 Questions  >  In quadrilateral ABCD, AO and BO are the bise... Start Learning for Free
In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D)
Most Upvoted Answer
In quadrilateral ABCD, AO and BO are the bisector of angle A and B res...
Proof:
We need to prove that angle AOB is half of angle CD.

Given:
- Quadrilateral ABCD
- AO and BO are the bisectors of angle A and B respectively

To Prove:
- Angle AOB is 1/2 angle CD

Proof:
- Let angle AOB be x and angle DCB be y
- Since AO and BO are bisectors of angle A and B respectively, we have:
- Angle AOC = Angle COB = (180 - x)/2
- Angle BOD = Angle DOA = (180 - y)/2
- Since the angles in a quadrilateral sum up to 360 degrees, we have:
- Angle AOC + Angle COB + Angle BOD + Angle DOA = 360
- (180 - x)/2 + (180 - x)/2 + (180 - y)/2 + (180 - y)/2 = 360
- 360 - x - y = 2x + 2y - 720
- Simplifying, we get:
- 3x + 3y = 540
- x + y = 180
- Since angle AOB is opposite to angle COD, we have:
- x + y = Angle COD
- Substituting the value of x + y, we get:
- Angle COD = 180
- Therefore, angle AOB is half of angle COD, i.e. angle AOB = 1/2 angle CD

Conclusion:
Hence, we have proved that angle AOB is half of angle CD in quadrilateral ABCD where AO and BO are bisectors of angle A and B respectively.
Community Answer
In quadrilateral ABCD, AO and BO are the bisector of angle A and B res...
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
Explore Courses for Class 9 exam

Top Courses for Class 9

In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D)
Question Description
In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D).
Solutions for In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) in English & in Hindi are available as part of our courses for Class 9. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) defined & explained in the simplest way possible. Besides giving the explanation of In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D), a detailed solution for In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) has been provided alongside types of In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) theory, EduRev gives you an ample number of questions to practice In quadrilateral ABCD, AO and BO are the bisector of angle A and B respectively. Prove that angle AOB=1/2 (angle C+D) tests, examples and also practice Class 9 tests.
Explore Courses for Class 9 exam

Top Courses for Class 9

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev