Note: Exercises preceded by an asterisk are of a more challenging nature.
In Exercises 1 to 4, write the converse, the inverse, and the contrapositive of each statement. When possible, classify the statement as true or false.
Two angles are complementary if the sum of their measures is
To find:
The converse, the inverse, and the contrapositive of each statement.
Given:
The given statement is,
Two angles are complementary if the sum of their measures is
Approach:
Conditional (or Implication) | If P, then Q. | |
Converse of conditional | If Q, then P. | |
Inverse of conditional | If not P, then not Q. | |
Contrapositive of conditional | If not Q, then not P. |
Consider the given statement,
Two angles are complementary if the sum of their measures is
The conditional statement of the given statement is,
If the sum of the measures of two angles is
The conditional statement is in “if P, then Q” form.
Here P is the sum of the measures of two angles is
Converse of conditional statement is,
If, two angles are complementary, then the sum of their measures is
This statement is true by the definition of complementary angles.
Inverse of conditional is,
If the sum of the measures of two angles is not
This statement is true by the definition of complementary angles
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