To prove that a quadrilateral STUV is a parallelogram, we can use several properties or criteria. Here are the most commonly accepted conditions that, if satisfied, will prove that STUV is indeed a parallelogram:
-
Opposite Sides are Equal: If both pairs of opposite sides (ST and UV, SU and TV) are equal in length, then STUV is a parallelogram.
-
Opposite Angles are Equal: If both pairs of opposite angles (∠S and ∠U, ∠T and ∠V) are equal, then STUV is a parallelogram.
-
One Pair of Opposite Sides are Equal and Parallel: If one pair of opposite sides (say ST and UV) is both equal in length and parallel, then STUV is a parallelogram.
-
Diagonals Bisect Each Other: If the diagonals (SU and TV) of STUV bisect each other at point O, then STUV is a parallelogram.
-
Using Vectors: If you can assign position vectors to the points S, T, U, and V such that the vector representations show that the vector from S to T is equal to the vector from V to U, and the vector from S to U is equal to the vector from T to V.
Any of these criteria can be used to prove that a quadrilateral STUV is a parallelogram.