Class 10 Exam > Class 10 Questions > ABC is an isosceles triangle right angled at ...
Start Learning for Free
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2?
Most Upvoted Answer
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)...
Community Answer
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)...
Understanding the Isosceles Right Triangle
An isosceles triangle has two sides of equal length. In triangle ABC, where angle C is a right angle, we have AC = BC.
Labeling the Triangle
- Let AC = BC = x (the lengths of the equal sides).
- Since triangle ABC is right-angled at C, AB is the hypotenuse.
Applying the Pythagorean Theorem
In any right triangle, the Pythagorean theorem states:
AB² = AC² + BC²
- Substituting the lengths:
- AB² = x² + x²
Simplifying the Equation
- This simplifies to:
- AB² = 2x²
Final Result
Thus, we conclude:
(AB)² = 2(AC)²
Conclusion
This proof demonstrates that in an isosceles triangle right-angled at C, the square of the length of the hypotenuse (AB) is twice the square of the length of either leg (AC).
An isosceles triangle has two sides of equal length. In triangle ABC, where angle C is a right angle, we have AC = BC.
Labeling the Triangle
- Let AC = BC = x (the lengths of the equal sides).
- Since triangle ABC is right-angled at C, AB is the hypotenuse.
Applying the Pythagorean Theorem
In any right triangle, the Pythagorean theorem states:
AB² = AC² + BC²
- Substituting the lengths:
- AB² = x² + x²
Simplifying the Equation
- This simplifies to:
- AB² = 2x²
Final Result
Thus, we conclude:
(AB)² = 2(AC)²
Conclusion
This proof demonstrates that in an isosceles triangle right-angled at C, the square of the length of the hypotenuse (AB) is twice the square of the length of either leg (AC).
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2?
Question Description
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2?.
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2?.
Solutions for ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? defined & explained in the simplest way possible. Besides giving the explanation of
ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2?, a detailed solution for ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? has been provided alongside types of ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? theory, EduRev gives you an
ample number of questions to practice ABC is an isosceles triangle right angled at C.Prove that (AB)^2=2(AC)^2? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup