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.
