Trapezoid PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Which statement is true?

A) The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

B) Trapezoid PQRS is not congruent to trapezoid P'Q'R'S'.

C) The area of trapezoid PQRS is less than the area of trapezoid P'Q'R'S'.

D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid P'Q'R'S'.

Answer: D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid P'Q'R'S'

Step-by-step explanation:

Since, By the definition of rotation about origin, When a figure is rotate 180° about the origin then we get a congruent figure to that figure.

Thus, when PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'.

Then trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

⇒ By the definition of congruence,

The corresponding sides and angle of trapezoid P'Q'R'S' are congruent to that of trapezoid PQRS.

⇒ ∠P' ≅ ∠P, ∠Q' ≅ ∠Q, ∠R' ≅ ∠R and ∠S' ≅ ∠S

⇒ Option D) is correct.

Note: P'Q'R'S' is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

Since, trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

⇒ Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid P'Q'R'S' = Area of trapezoid PQRS

Thus, Option C) is also incorrect.