Given: Quadrilateral ABCD with BC = 3, AB || CD
To prove:
ABCD is a parallelogram.
AC + BD = AD.
Proof:
1)
Since BC = 3 and AB || CD, we have AB = CD (Alternate Interior Angles Theorem).
Thus, ABCD is a parallelogram (opposite sides of a parallelogram are equal).
In parallelogram ABCD:
AC || BD (opposite sides of a parallelogram are parallel)
AC = BD (opposite sides of a parallelogram are equal)
AD = BC = 3 (given)
Therefore, AC + BD = AD (In a parallelogram, the sum of the diagonals is equal to the sum of the two opposite sides).
Hence, AC + BD = AD.
