Class 9 Exam > Class 9 Questions > O is any point in the interior of a square AB...
Start Learning for Free
O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .?
Verified Answer
O is any point in the interior of a square ABCD such that OAB is an eq...
Given:OAB is equilateral triangle. to prove:OCD is an isosceles triangle. construction:from point O, draw line from O to the points A,B,C,D. proof:line AC & BD are 2 diagonals equal. point O bisects all the diagonals. thus,AO=BO=CO=DO...CO is same as DO which proves that, OCD is isosceles.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
O is any point in the interior of a square ABCD such that OAB is an eq...
Proof that Triangle OCD is Isosceles:
- Since OAB is an equilateral triangle, all sides are equal in length. Therefore, OA = AB = OB.
- Since O is the midpoint of AB, it divides the square diagonally into two equal parts. So, AO = OB.
- In triangle AOC, AO = OC (as O is the midpoint of AC in the square).
- Combining the above two points, we have AO = OC = OB. Therefore, triangle OCD is isosceles.
Finding the Measure of Angle OCD:
- Since triangle OCD is isosceles, OC = OD. Therefore, angles OCD and ODC are equal as they are base angles of an isosceles triangle.
- The sum of angles in a triangle is 180 degrees. So, in triangle OCD, we have: OCD + ODC + O = 180 degrees.
- Since OAB is an equilateral triangle, angle AOB is 60 degrees.
- Since square ABCD is a 90-degree angle, angle AOC is 90 degrees.
- Substituting these values into the equation from the previous point, we get: OCD + 60 + 90 = 180 degrees.
- Solving for OCD, we find: OCD = 30 degrees.
Therefore, triangle OCD is an isosceles triangle with angle OCD measuring 30 degrees.
- Since OAB is an equilateral triangle, all sides are equal in length. Therefore, OA = AB = OB.
- Since O is the midpoint of AB, it divides the square diagonally into two equal parts. So, AO = OB.
- In triangle AOC, AO = OC (as O is the midpoint of AC in the square).
- Combining the above two points, we have AO = OC = OB. Therefore, triangle OCD is isosceles.
Finding the Measure of Angle OCD:
- Since triangle OCD is isosceles, OC = OD. Therefore, angles OCD and ODC are equal as they are base angles of an isosceles triangle.
- The sum of angles in a triangle is 180 degrees. So, in triangle OCD, we have: OCD + ODC + O = 180 degrees.
- Since OAB is an equilateral triangle, angle AOB is 60 degrees.
- Since square ABCD is a 90-degree angle, angle AOC is 90 degrees.
- Substituting these values into the equation from the previous point, we get: OCD + 60 + 90 = 180 degrees.
- Solving for OCD, we find: OCD = 30 degrees.
Therefore, triangle OCD is an isosceles triangle with angle OCD measuring 30 degrees.
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
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .?
Question Description
O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? 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 O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .?.
O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? 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 O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .?.
Solutions for O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? 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 O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? defined & explained in the simplest way possible. Besides giving the explanation of
O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .?, a detailed solution for O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? has been provided alongside types of O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? theory, EduRev gives you an
ample number of questions to practice O is any point in the interior of a square ABCD such that OAB is an equilateral triangle. show that triangle OCD is an isosceles triangle. also find the measure of angle OCD .? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup