find the converse and determine if it is true or false. statement: obtuse angles are not right angles
True, obtuse angles' degrees are greater than 90 and less than 180 and a right angle is exactly 90 degrees
Oh, I love playing around with angles! Now, let's have some fun with the converse of that statement. The converse says, "If an angle is not a right angle, then it is obtuse." So, let's see if this is true or false.
The original statement is, "Obtuse angles are not right angles." This means any angle that is not a right angle is considered obtuse. So, let's think about it. Is every angle that is not a right angle necessarily obtuse? Well, no! There are other types of angles, like acute angles or straight angles, that are not obtuse.
Therefore, the converse, "If an angle is not a right angle, then it is obtuse," is FALSE. Because there are other types of angles that are not obtuse, such as acute angles or straight angles. Remember, angles can be quite tricky!
To find the converse of the statement "obtuse angles are not right angles," we need to interchange the hypothesis and conclusion. The converse of the statement is: "Right angles are not obtuse angles."
As for determining the truth value of the converse, we need to assess whether all right angles are not obtuse angles. This is true because right angles are defined as having a measure of exactly 90 degrees, while obtuse angles have a measure greater than 90 degrees.
Therefore, the converse ("Right angles are not obtuse angles") is true.
To find the converse of a statement, you need to switch the hypothesis (the "If" part) and the conclusion (the "Then" part) of the original statement.
The original statement is: "Obtuse angles are not right angles."
The converse of this statement is: "Right angles are not obtuse angles."
To determine if the converse is true or false, you need to evaluate whether the swapped statement holds. In this case, the converse is actually also true. A right angle is defined as an angle that measures exactly 90 degrees, while an obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Therefore, a right angle cannot be an obtuse angle.
So, in summary, the converse statement, "Right angles are not obtuse angles," is true.