Question

question 1 of 10
if both pairs of opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.

a. true

b. false

Explanation:

To determine if the statement is true or false, we recall the properties of a parallelogram. In a parallelogram, opposite angles are equal. However, for a quadrilateral to be a parallelogram, a more relevant property is that consecutive angles are supplementary (since opposite sides are parallel, consecutive angles are same - side interior angles and thus supplementary). The given statement says that if both pairs of opposite angles are supplementary, then the quadrilateral is a parallelogram. But a quadrilateral with both pairs of opposite angles supplementary is not necessarily a parallelogram. For example, a cyclic quadrilateral (a quadrilateral inscribed in a circle) has both pairs of opposite angles supplementary, but not all cyclic quadrilaterals are parallelograms (only cyclic parallelograms, which are rectangles, are both cyclic and parallelograms). So the statement is false.

Answer:

B. False