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“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?
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“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.
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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.
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“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.
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“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?
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“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?.
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