Question

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

Answer 1

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.