Which transformation will map an isosceles trapezoid onto itself?
a. rotation by 180° about its center
b. reflection across a diagonal
c. reflection across a line joining the midpoints of the nonparallel sides
d.
rotation by 360° about its center

The answer is (d) rotation by 360° about its center.

Step-by-step explanation:  As shown in the attached figure, AB and CD are parallel sides of an isosceles trapezoid ABCD with center 'O' and AD and BC are equal and non-parallel sides.

(i) If ABCD is rotated by 180° about its center, then the new figure will not coincide with the original one. So, this option is not correct.

(ii) If ABCD is reflected across a diagonal, then also the new figure will be reverse of the original one and so this option is also incorrect.

(iii) If ABCD is reflected across a line joining the mid-points of the non-parallel sides, then also the two figures will be opposite of each other. This option will also not work.

(iv) If we rotate ABCD through 360° about center 'O', the both the figures will coincide with each other.

Thus, the correct option is (d) rotation by 360° about its center.

is there any photos or whatever?

b. 2 and 4

step-by-step explanation: