Question

Select the correct answer.

Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?



A.
He needs to show only that the diagonals are perpendicular.
B.
He needs to show only that the diagonals are perpendicular and congruent.
C.
He needs to show only that the diagonals are perpendicular and bisect each other.
D.
He needs to show that the diagonals are perpendicular, congruent, and bisect each other.

Answer 1

Adam can prove that quadrilateral PQRS inscribed in a circle is a square by showing that the diagonals are perpendicular, congruent, and they bisect each other, as per option D.

Step-by-step explanation:

To prove that quadrilateral PQRS is a square when inscribed in circle O, Adam must show that the diagonals of PQRS have specific properties that are characteristic of a square. Adam should demonstrate that the diagonals are perpendicular to each other, they are congruent (that is, they have equal length), and they bisect each other (each diagonal cuts the other into two equal parts). To satisfy all the conditions that define a square, option D is correct: Adam must show that the diagonals are perpendicular, congruent, and bisect each other.

Answer 2

Answer: D

Step-by-step explanation:

You need to prove that the diagonals bisect each other to prove it's a parallelogram.

Now, to prove it's a square, you need to prove it's both a rectangle and a rhombus.

• To prove it's a rectangle, you need to prove the diagonals are congruent.
• To prove it's a rhombus, you need to prove the diagonals are perpendicular.