Edwidge draws parallelogram STUV with a center at O. What must be true to prove that STUV is a parallelogram?(1 point) Responses ST¯¯¯¯¯¯¯≅UV¯¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯ line segment cap s cap t is congruent to line segment cap u cap v A n d line segment cap t cap u comma line segment cap u cap v and line segment cap t cap u is congruent to line segment cap s cap v SO¯¯¯¯¯¯¯≅VO¯¯¯¯¯¯¯¯ and TO¯¯¯¯¯¯¯ ≅UO¯¯¯¯¯¯¯¯ line segment cap s cap o is congruent to line segment cap v cap o and line segment cap t cap o comma line segment cap v cap o A n d line segment cap t cap o is congruent to line segment cap u cap o SO¯¯¯¯¯¯¯≅TO¯¯¯¯¯¯¯ and UO¯¯¯¯¯¯¯¯ ≅VO¯¯¯¯¯¯¯¯ line segment cap s cap o is congruent to line segment cap t cap o A n d line segment cap u cap o comma line segment cap t cap o and line segment cap u cap o is congruent to line segment cap v cap o ST¯¯¯¯¯¯¯≅TU¯¯¯¯¯¯¯ and UV¯¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯
1 answer
To prove that STUV is a parallelogram, you typically need to establish that either the opposite sides are congruent or that the diagonals bisect each other.
Given the choices, the response that suitably demonstrates that STUV is a parallelogram is:
ST̅̅̅̅̅ ≅ UV̅̅̅̅̅̅ and TU̅̅̅̅̅ ≅ SV̅̅̅̅̅.
This statement shows that both pairs of opposite sides are congruent, which is a criterion for parallelograms. Therefore, it must be true that STUV is a parallelogram if these conditions are satisfied.
