Question

which biconditional statement is true?
a. two angles are supplementary if and only if they form a linear pair.
b. a quadrilateral is a rectangle if and only if it has four congruent sides.
c. an integer is a prime number if and only if it is odd.
d. two lines are parallel if and only if they have the same slope.

Explanation:

• Option A: Supplementary angles sum to 180°, but not all supplementary angles form a linear pair (e.g., two angles in different planes can be supplementary without being adjacent). So this biconditional is false.
• Option B: A rectangle has four right angles, but a quadrilateral with four congruent sides is a rhombus (a square is a special case, but not all rectangles are rhombuses). So this biconditional is false.
• Option C: 2 is a prime number but it is even, so not all prime numbers are odd, and not all odd numbers are prime (e.g., 9). So this biconditional is false.
• Option D: For non - vertical lines in a coordinate plane, two lines are parallel if and only if they have the same slope. Vertical lines are parallel and have an undefined slope (and we can consider their "slope" property in the context of parallelism). So this biconditional is true.

Answer:

D. Two lines are parallel if and only if they have the same slope.