if angles are congruent then they are equal in measure. can someone write the converse, the inverse and the contrapositive.
if a then b
converse: if b then a
inverse: if ~a then ~b
contrapositive: if ~b then ~a
better review these definitions
Sure! The statements regarding angles can be written as follows:
Statement: If angles are congruent, then they are equal in measure.
Converse: If angles are equal in measure, then they are congruent.
Inverse: If angles are not congruent, then they are not equal in measure.
Contrapositive: If angles are not equal in measure, then they are not congruent.
Certainly! Let's break down the statements and explain how to write the converse, inverse, and contrapositive of the given statement.
The given statement is: "If angles are congruent, then they are equal in measure."
1. Converse: To write the converse of a conditional statement, you need to switch the hypothesis and the conclusion. So, the converse of the given statement would be: "If angles are equal in measure, then they are congruent."
2. Inverse: To write the inverse of a conditional statement, you need to negate both the hypothesis and the conclusion. Negating a statement means stating the opposite of it. So, the inverse of the given statement would be: "If angles are not congruent, then they are not equal in measure."
3. Contrapositive: To write the contrapositive of a conditional statement, you need to both switch and negate the hypothesis and the conclusion. So, the contrapositive of the given statement would be: "If angles are not equal in measure, then they are not congruent."
To summarize:
- The converse switches the hypothesis and the conclusion.
- The inverse negates both the hypothesis and the conclusion.
- The contrapositive switches and negates both the hypothesis and the conclusion.
Each of these statements may or may not be logically equivalent to the original statement, depending on the specific situations being discussed.