Question

Match each statement with its contrapositive.

a) If a figure isn't a pentagon, then the sum of its interior angles isn't 540°.
b) If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon.
c) If two figures aren't congruent, then their corresponding sides aren't equal.
d) If the corresponding sides of two figures aren't equal, then the two figures aren't congruent.

Answer 1

To match each statement with its contrapositive, we negated and swapped the hypothesis and conclusion of each conditional statement.

Step-by-step explanation:

The task is to match each conditional statement with its contrapositive. The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then swapping them.

Let's break down each conditional statement provided:

1. If a figure isn't a pentagon, then the sum of its interior angles isn't 540°.
2. If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon.
3. If two figures aren't congruent, then their corresponding sides aren't equal.
4. If the corresponding sides of two figures aren't equal, then the two figures aren't congruent.

The contrapositives will therefore be:

1. If the sum of its interior angles is 540°, then the figure is a pentagon. (contrapositive of b)
2. If a figure is a pentagon, then the sum of its interior angles is 540°. (contrapositive of a)
3. If the corresponding sides of two figures are equal, then the two figures are congruent. (contrapositive of d)
4. If two figures are congruent, then their corresponding sides are equal. (contrapositive of c)