Question

Let ABCD be a parallelogram (Fig 3.23). Copy it on a tracing sheet. Name this copy as A'B'C'D'. Place A'B'C'D' on ABCD. Pin them together at the point where the diagonals meet. Rotate the transparent sheet by 180°. The parallelograms still coincide; but you now find A' lying exactly on C and vice-versa; similarly B' lies on D and vice-versa.

Does this tell you anything about the measures of the angles A and C? Examine for angles B and D. State your findings.
a) The opposite angles of a parallelogram are of equal measure.
b) The adjacent angles of a parallelogram are supplementary.
c) The sum of angles A and C is 180°.
d) The sum of angles B and D is 360°.

Answer 1

Rotating a traced parallelogram 180° proves that opposite angles in a parallelogram are equal and adjacent angles are supplementary. The sum of opposite angles A and C, and B and D, is 180°, not 360° as suggested in one option.

Step-by-step explanation:

When a student traces a parallelogram ABCD to create a copy A'B'C'D' and then rotates it by 180° around the point where diagonals meet, A' ends up on C and B' on D. This geometric behavior demonstrates some key properties of parallelograms: