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(a)
To state: The property that proves that the quadrilateralQUADis a parallelogram.
(a)
Answer to Problem 1PSA
QUADis a parallelogram because its diagonals bisect each other.
Explanation of Solution
Given:The diagonalsAQand UDof a quadrilateral QUADbisects each other.
QUADis a parallelogram because its diagonals bisect each other.
(b)
To state: The property that proves that the quadrilateral QUADwith it’s a pair of opposite sides equal and parallel, is a parallelogram.
(b)
Answer to Problem 1PSA
A pair of opposite sides in the given quadrilateral QUADis congruent and parallel so it is a parallelogram.
Explanation of Solution
Given:In quadrilateral QUAD,
Here a pair of opposite sides is congruent and parallel so given quadrilateral QUADis a parallelogram.
(c)
To state: The property that proves that the quadrilateral QUADwith its both pairs of opposite sides as equal, is a parallelogram.
(c)
Answer to Problem 1PSA
Both pairs of opposite sides in the given quadrilateral QUADare congruent to each other so it is a parallelogram.
Explanation of Solution
Given:In quadrilateral QUAD,
Here both pairs of opposite sides are congruent to each other so the given quadrilateral QUADis a parallelogram.
(d)
To state: The property that proves that the quadrilateral QUADwith its both pairs of opposite sides as equal, is a parallelogram.
(d)
Answer to Problem 1PSA
In this case, none of the properties of a parallelogram is being satisfied by the given quadrilateral QUADso it is not a parallelogram.
Explanation of Solution
Given:In quadrilateral QUAD,
A quadrilateral can be a parallelogram only if it satisfies one of the given properties,
(i) If both pairs of opposite sides of a quadrilateral are parallel.
(ii) If both pairs of opposite sides of a quadrilateral are congruent.
(iii) If both pairs of opposite
(iv)If the diagonals of a quadrilateral bisect each other.
(v) If one pair of opposite sides of a quadrilateral are both parallel and congruent.
But here none of the properties being satisfied so given quadrilateral QUADis not a parallelogram.
(e)
To state: The property that proves that the quadrilateral QUADwith a pair of opposite sides as parallel and a pair of alternate interior angles as equal, is a parallelogram.
(e)
Answer to Problem 1PSA
Both pairs of opposite sides in the given quadrilateral QUADare parallel to each other so it is a parallelogram.
Explanation of Solution
Given:In quadrilateral QUAD,
As given,
Hence both pairs of opposite sides in the given quadrilateral QUADare parallel to each other so it is a parallelogram.
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