Question

Conditional: If p, then q.

Converse: If q, then p
Inverse: If not p, then not q
Contrapositive: If not q, then not p.
Biconditional:Pif and only if q
Which of the following statements is a biconditional statement?
a. Two lines are parallel if and only if they never intersect.
b. If a figure is a chord, then it is a line segment.
c If the measure of an angle is 132°, then it is obtuse.
d. A figure that has four equal sides is a square.

Answer 1

In the provided options, the biconditional statement is 'Two lines are parallel if and only if they never intersect', because the relationship between being parallel and never intersecting meets the necessary and sufficient conditions of a biconditional statement. The correct answer is a. Two lines are parallel if and only if they never intersect.

Step-by-step explanation:

The question asks which of the given statements is a biconditional statement. A biconditional statement is a logical statement that is true if and only if both components are true. It is represented as 'P if and only if Q', meaning P is true if Q is true, and Q is true if P is true.

In the context of the provided options, the biconditional statement is 'Two lines are parallel if and only if they never intersect' (a). This is because for two lines to be considered parallel, they must satisfy the condition of never intersecting, and conversely, if two lines never intersect, they are considered parallel.

Other options do not present a necessary and sufficient condition relationship as required by a biconditional. For instance, all chords are line segments (b) but not all line segments are chords; similarly, if an angle measures 132°, it is indeed obtuse (c), but not all obtuse angles measure 132°.

Lastly, a figure with four equal sides is a square (d), but it must also have four right angles to be a square; therefore, having four equal sides alone is not sufficient.