Question

What is the contrapositive of the statement “If two triangles are identical, then these are similar.”?
A. If two triangles are not similar, then these 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.

Answer 1

Hint: Use the definition of the contrapositive concept of mathematical logic and convert the given statement into the contrapositive statement.

Formula used:
The contrapositive of a conditional statement, interchange the original hypothesis and the conclusion of the statement.
The negation of a statement is the opposite of the original statement.
The negation is represented by a symbol: \[\sim \]

Complete step by step solution:
The given statement is “If two triangles are identical, then these are similar.”
Let’s consider,
\[p:\] two triangles are identical
\[q:\] two triangles are similar
So, the symbolic representation of the given statement is: \[p \to q\]
Now apply the definition of the contrapositive concept of mathematical logic.
Then the contrapositive representation is: \[\sim q \to \sim p\]

The negation statements of the above statements are:
\[\sim p :\] two triangles are not similar
\[\sim q :\] two triangles are not identical
Therefore, the word representation of the contrapositive statement is,
\[\sim q \to \sim p\]: If two triangles are not similar, then these are not identical.

Hence the correct option is A.

Note: Students often get confused and consider contrapositive as the negation.
A contrapositive statement is a negation of terms of a converse statement.
Statement: \[a \to b\]
Contrapositive statement: \[\sim b \to \sim a\]