Final answer:
The correct statement is d. The perimeter of triangle QRS is equal to the perimeter of triangle Q'R'S', as reflections preserve the length of sides and therefore the perimeter.
Step-by-step explanation:
When triangle QRS is reflected across the x-axis to produce triangle Q'R'S', certain properties of the triangle remain the same due to the nature of reflection. Reflection over the x-axis changes the sign of the y-coordinates of the points but keeps the x-coordinates the same. This transformation results in a mirror image of the original shape, and since it's a rigid motion, it preserves the distances between points and the measures of angles.
a. The length of side RS is equal to the length of side Q'R'. This statement is incorrect because RS corresponds to R'S' after reflection, not Q'R'.
b. The length of side QR is equal to the length of side Q'S'. This is incorrect because QR corresponds to Q'R' after reflection, not Q'S'.
c. The measure of angle QRS is equal to the measure of angle R'S'Q'. This is incorrect because angle measures are preserved in reflection, but the angle notation should be consistent; QRS corresponds to Q'R'S'.
d. The perimeter of triangle QRS is equal to the perimeter of triangle Q'R'S'. This statement is true because reflections are rigid motions that do not change the length of sides, hence the perimeters remain equal.
Learn more about Reflections in Geometry