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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.

(1) The sides of Q have the same length. (2) The diagonals of Q have the same length

In a parallelogram, not all the sides have the same length from what I understand. Or am I missing something?

Parallelogram CAN have all 4 sides of equal length.

ParallelogramA 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 _________________

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?

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?

If a parallelogram has equal sides it is a rhombus but rhombus is not necessary to have equal diagonals, or in other words not all rhombuses are squares:

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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Is quadrilateral Q a square? (1) The sides of Q have the same length. (2) The diagonals of Q have the same length

C

Here il post u a drawing.

This is an incorrect explanation cause a hexagon is not a quadrilateral and instead a uniform trapezium or a rectangle is a better alternative
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Last edited by JusTLucK04 on 05 Jun 2014, 04:20, edited 1 time in total.