Which conditional has the same truth value as its converse?
If x = 7, then |x| = 7.
If a figure is a square, then it has four sides.
If x – 17 = 4, then x = 21.
If an angle has a measure of 80°, then it is acute.
If a figure is a square, then it has four sides.
The conditional statement "If x = 7, then |x| = 7" has the same truth value as its converse.
To determine which conditional has the same truth value as its converse, we need to identify the converse of each conditional statement and then compare their truth values.
1. If x = 7, then |x| = 7.
Converse: If |x| = 7, then x = 7.
The truth value of the original statement and its converse is the same. Both are true because if x is equal to 7, then the absolute value of 7 is indeed 7.
2. If a figure is a square, then it has four sides.
Converse: If a figure has four sides, then it is a square.
The truth value of the original statement and its converse is not the same. The original statement is true since all squares do have four sides, but the converse is false since there are other shapes with four sides that are not squares (e.g., rectangles).
3. If x – 17 = 4, then x = 21.
Converse: If x = 21, then x – 17 = 4.
The truth value of the original statement and its converse is the same. Both are true because if x minus 17 equals 4, then x must be equal to 21.
4. If an angle has a measure of 80°, then it is acute.
Converse: If an angle is acute, then it has a measure of 80°.
The truth value of the original statement and its converse is not the same. The original statement is true because an angle of 80° is indeed acute, but the converse is false since there are other acute angles with different measures.
Therefore, the conditional that has the same truth value as its converse is:
If x = 7, then |x| = 7.