Question

In quadrilateral PQRS, consecutive angles are supplementary, Which of the following statements are true?Both diagonals are angle bisectors.The diagonals bisect each other,Both pairs of opposite angles are congruent.

Answer 1

It's not necessarily true that the diagonals in a quadrilateral with supplementary consecutive angles are angle bisectors, bisect each other, or that opposite angles are congruent. These characteristics are typical of parallelograms but aren't universally applicable to all quadrilaterals with the given angle property.

Step-by-step explanation:

The question is about a quadrilateral where consecutive angles are supplementary. In such a quadrilateral, it is not necessarily true that both diagonals are angle bisectors or that they bisect each other. However, it is characteristic for a parallelogram to have supplementary consecutive angles. In parallelograms specifically, opposite angles are congruent, but this doesn't extend to all quadrilaterals with supplementary consecutive angles.

In terms of the statements provided:

• Both diagonals are angle bisectors: This is usually true for kites and some other specific quadrilateral types, but not for all quadrilaterals with supplementary angles.
• The diagonals bisect each other: This is true for parallelograms, including rectangles, rhombuses, and squares.
• Both pairs of opposite angles are congruent: This is true for parallelograms.

Without additional information, we cannot definitively state that all the provided statements are true for the described quadrilateral.