Find the contrapositive and determine if it is true or false.
Statement: Obtuse angles are not right angles.
Obtuse angles' degrees are greater than 90, and less than 180, and a right angle is exactly 90 degrees. Meaning the answer is True!
If p→q
then the contrapositive is ~q → ~p
and has the same truth value as p→q.
To find the contrapositive of a statement, we first need to rewrite the statement in the form "If A, then B."
The original statement, "Obtuse angles are not right angles," can be rewritten as, "If an angle is obtuse, then it is not a right angle."
The contrapositive of a statement is formed by negating both the hypothesis and the conclusion of the original statement and switching their order.
Negating the hypothesis ("If an angle is obtuse") gives us "If an angle is not obtuse," and negating the conclusion ("it is not a right angle") gives us "it is not a right angle."
Switching the order and combining these two parts gives us the contrapositive: "If an angle is not a right angle, then it is not obtuse."
In this case, the contrapositive statement is "If an angle is not a right angle, then it is not obtuse."
Now, let's determine if the contrapositive is true or false. The contrapositive can be read as "If an angle is not a right angle, then it is not obtuse." This statement is true because all right angles are not obtuse angles.
To find the contrapositive of a statement, we first need to understand the original statement. The original statement is "Obtuse angles are not right angles."
The contrapositive of a statement is formed by negating both the hypothesis and the conclusion of the original statement, and then swapping their positions. The hypothesis is the part that comes after "if" in the original statement, and the conclusion is the part that comes after "then."
In the original statement, the hypothesis is "Obtuse angles" and the conclusion is "not right angles."
To form the contrapositive, we need to negate both the hypothesis and the conclusion and then swap their positions.
Negating "Obtuse angles" gives us "Not obtuse angles."
Negating "not right angles" gives us "Right angles."
Swapping their positions, the contrapositive of the original statement is "If an angle is not obtuse, then it is a right angle."
Now, let's determine if the contrapositive is true or false. The contrapositive is saying that any angle that is not obtuse is a right angle. This is not always true, as there are other types of angles that are not obtuse, such as acute angles. Therefore, the contrapositive is false.