JEE Exam > JEE Questions > “If two triangles are congruent, then their ...
Start Learning for Free
“If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement is
- a)If areas of two triangles are not equal then they are congruent
- b)If two triangles are not congruent then their areas are equal
- c)If two triangles are not congruent then their areas are not equal
- d)If areas of two triangles are equal then they are congruent
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
“If two triangles are congruent, then their areas are equal" is the g...
Key Idea: Use p → g then inverse of ft is ~ p → q and contrapositive is ~ q → p.
View all questions of this test
The inverse of the gi\ren statement: "If two triangles are not congruent, then their areas are not equal”
∴ The contrapositive of the inverse of the given statement: If areas of two triangles are equal, then they are congruent.
Most Upvoted Answer
“If two triangles are congruent, then their areas are equal" is the g...
Contrapositive of the Given Statement:
The contrapositive of the given statement "If two triangles are congruent, then their areas are equal" is:
Option D: If areas of two triangles are equal then they are congruent
Explanation:
Understanding the Contrapositive:
The contrapositive of a statement switches the hypothesis and conclusion of the original statement and negates both. In this case, the original statement is about congruent triangles and their areas being equal. Therefore, the contrapositive statement talks about equal areas leading to congruent triangles.
Breaking Down Option D:
- The statement "If areas of two triangles are equal then they are congruent" directly corresponds to the contrapositive of the original statement.
- This means that if the areas of two triangles are equal, then the triangles must be congruent to each other.
- This relationship highlights the fact that equal areas in triangles imply congruence, which is a fundamental concept in geometry.
Conclusion:
The contrapositive statement, as presented in option D, effectively captures the logical relationship between the congruence of triangles and the equality of their areas. It serves as a valid alternative way of expressing the same mathematical concept stated in the original statement.
The contrapositive of the given statement "If two triangles are congruent, then their areas are equal" is:
Option D: If areas of two triangles are equal then they are congruent
Explanation:
Understanding the Contrapositive:
The contrapositive of a statement switches the hypothesis and conclusion of the original statement and negates both. In this case, the original statement is about congruent triangles and their areas being equal. Therefore, the contrapositive statement talks about equal areas leading to congruent triangles.
Breaking Down Option D:
- The statement "If areas of two triangles are equal then they are congruent" directly corresponds to the contrapositive of the original statement.
- This means that if the areas of two triangles are equal, then the triangles must be congruent to each other.
- This relationship highlights the fact that equal areas in triangles imply congruence, which is a fundamental concept in geometry.
Conclusion:
The contrapositive statement, as presented in option D, effectively captures the logical relationship between the congruence of triangles and the equality of their areas. It serves as a valid alternative way of expressing the same mathematical concept stated in the original statement.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
“If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer?
Question Description
“If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer?.
“If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer?.
Solutions for “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
“If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice “If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, toe inverse of the given statement isa)If areas of two triangles are not equal then they are congruentb)If two triangles are not congruent then their areas are equalc)If two triangles are not congruent then their areas are not equald)If areas of two triangles are equal then they are congruentCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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