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Which of the following is the contrapositive of if two triangles are identical, then these are similar?
- a)if two triangles are not similar, they are not identical
- b)If two triangles are not identical, then these are not similar
- c)If two triangles are not identical, then these are similar
- d)If two triangles are not similar, then these are identical
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following is the contrapositive of if two triangles are i...
Consider the following statements
p: Two triangles are identical.
q: Two triangles are similar.
Clearly, the given statement in symbolic form is p ⇒ q.
Therefore, its contrapositive is given by ∼ q ⇒ ∼ p
Now,
∼p: two triangles are not identical.
∼q: two triangles are not similar.
Therefore, ~ q ⇒ ~ p: If two triangles are not similar, then these are not identical.
p: Two triangles are identical.
q: Two triangles are similar.
Clearly, the given statement in symbolic form is p ⇒ q.
Therefore, its contrapositive is given by ∼ q ⇒ ∼ p
Now,
∼p: two triangles are not identical.
∼q: two triangles are not similar.
Therefore, ~ q ⇒ ~ p: If two triangles are not similar, then these are not identical.
Most Upvoted Answer
Which of the following is the contrapositive of if two triangles are i...
The contrapositive of a conditional statement switches the hypothesis and conclusion and negates both. In this case, the original statement is "If two triangles are identical, then these are similar." To find the contrapositive, we need to switch the hypothesis ("two triangles are identical") and conclusion ("these are similar") and negate both.
Let's analyze each option to determine which one is the contrapositive:
a) If two triangles are not similar, they are not identical.
b) If two triangles are not identical, then these are not similar.
c) If two triangles are not identical, then these are similar.
d) If two triangles are not similar, then these are identical.
The correct answer is option a) "If two triangles are not similar, they are not identical."
Explanation:
To understand why option a) is the contrapositive, we need to break down the original statement and its negation:
Original Statement: If two triangles are identical, then these are similar.
Negation: It is not true that if two triangles are identical, then these are similar.
Now let's switch the hypothesis and conclusion and negate both:
Contrapositive: If two triangles are not similar, they are not identical.
This is the contrapositive of the original statement. It is important to note that the contrapositive has the same truth value as the original statement. In other words, if the original statement is true, then the contrapositive is also true, and vice versa.
Therefore, option a) is the correct answer as it correctly represents the contrapositive of the given statement.
Let's analyze each option to determine which one is the contrapositive:
a) If two triangles are not similar, they are not identical.
b) If two triangles are not identical, then these are not similar.
c) If two triangles are not identical, then these are similar.
d) If two triangles are not similar, then these are identical.
The correct answer is option a) "If two triangles are not similar, they are not identical."
Explanation:
To understand why option a) is the contrapositive, we need to break down the original statement and its negation:
Original Statement: If two triangles are identical, then these are similar.
Negation: It is not true that if two triangles are identical, then these are similar.
Now let's switch the hypothesis and conclusion and negate both:
Contrapositive: If two triangles are not similar, they are not identical.
This is the contrapositive of the original statement. It is important to note that the contrapositive has the same truth value as the original statement. In other words, if the original statement is true, then the contrapositive is also true, and vice versa.
Therefore, option a) is the correct answer as it correctly represents the contrapositive of the given statement.
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Which of the following is the contrapositive of if two triangles are identical, then these are similar?a)if two triangles are not similar, they are not identicalb)If two triangles are not identical, then these are not similarc)If two triangles are not identical, then these are similard)If two triangles are not similar, then these are identicalCorrect answer is option 'A'. Can you explain this answer?
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