Question

11 multiple - choice 2 points which of the following biconditional statements are true? angles are supplementary if and only if their sum is 180 degrees a number is a whole number if and only if it is a natural number. points are collinear if and only if they are coplanar. angles are congruent if and only if they are vertical angles. clear my selection

Explanation:

1. Recall the definitions:

• Supplementary angles are defined as two - angles whose sum is 180 degrees. So, the statement "Angles are supplementary if and only if their sum is 180 degrees" is true by definition.
• Natural numbers are positive integers (1, 2, 3,...), while whole numbers include 0 and positive integers (0, 1, 2, 3,...). So, a number can be a whole number but not a natural number (e.g., 0), and the statement "A number is a whole number if and only if it is a natural number" is false.
• Collinear points lie on the same line, and coplanar points lie on the same plane. Points can be coplanar but not collinear, so the statement "Points are collinear if and only if they are coplanar" is false.
• Congruent angles have the same measure, and vertical angles are congruent, but not all congruent angles are vertical angles. So, the statement "Angles are congruent if and only if they are vertical angles" is false.

Answer:

Angles are supplementary if and only if their sum is 180 degrees.