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

The correct option is 4.

Step-by-step explanation:

The non parallel sides of an isosceles trapezoid are congruent.

The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if

1. Reflection across a line joining the midpoints of parallel sides.

2. Rotation by 360° about its center.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.

If we reflect the trapezoid across a diagonal, then the resultant figure will be a parallelogram.

If we reflect across a line joining the midpoints of the nonparallel sides, then the parallel sides will interchanged.

After rotation by 360° about the center, we always get an onto figure.

Therefore option 4 is correct.

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

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

(i) If ABCD is rotated by 180° about its centre, 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 centre 'O', the both the figures will coincide with each other.

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

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