Parallelogram CAN have all 4 sides of equal length.

Parallelogram A quadrilateral with two pairs of parallel sides.

Properties and Tips
• Opposite sides of a parallelogram are equal in length.
• Opposite angles of a parallelogram are equal in measure.
• Opposite sides of a parallelogram will never intersect.
• The diagonals of a parallelogram bisect each other.
• Consecutive angles are supplementary, add to 180°.
• The area, \(A\), of a parallelogram is \(A = bh\), where \(b\) is the base of the parallelogram and \(h\) is its height.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds:
• A rectangle is a parallelogram but with all angles fixed at 90°
• A rhombus is a parallelogram but with all sides equal in length
• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

For other properties check polygons chapter of Math Book: math-polygons-87336.html
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you can imagine four sticks with same length that are pinned by hinges. you can easily transform the square to a different rhombuses and even to a line.

Statement 1 is not sufficient since a rhombus has 4 equal sides as well.

Statement 2 is not sufficient since a rectangle has equal diagonals.

Statements 1 and 2 are sufficient.

HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?

A is insufficient cause rhombus is a quadrilateral with four sides & diagonals of dfferent lengths
B is insufficient cause a uniform Trapezoid has both the diagonals equal..

C is sufficient as trapezoid and rhombus are both eliminated.Hence a square
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Statement I is insufficient:

Rhombus have same lengths and so does a square.

Statement II is insufficient:

Sides may or may not be same.

Combining is sufficient:

If sides are same and diagonals are same which means all the sides must intersect at ninety degrees hence answer is c.
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Bumping for DS Butler project.
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