Tofind:the condition that does not guarantee the quadrilateral as parallelogram.
Answer to Problem 5STP
Choice D is correct because, it does not include congruent opposite sides.
Explanation of Solution
Given:
Concept used:
There are six important properties of parallelograms to know:
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
If one angle is right, then all angles are right.
The diagonal of a parallelogram bisects each other.
Each diagonal of a parallelogram separates it into two congruent triangles.
Calculation:
The condition would not guarantee that a quadrilateral is a parallelogram. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Therefore, choice A is not correct. If both the pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Therefore, choice B is not correct. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram therefore, the choice C is not correct. If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.
Hence, the choice D is correct because, it does not include congruent opposite sides.
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