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you can build one figure and see what you can get. Place 4 equal sticks on a table. The sticks can be 4 new pencils, or 4 new toothpicks, for example -- whatever is convenient to put your hands on in the house. First form a square with the sticks touching end-to-end; the square has 90 degrees (right angles) at the corners. Next move a pair of opposite corners equally toward one another, with the sticks pivoted at the corners and remained touching. You get a diamond shape, or a kite. Since you have disturbed the corners, the angles are no longer 90 degrees. Q.E.D.

Q: What quadrilateral has four equal sides and sometimes but not always has four right angles?

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Diagonally opposite pairs of angles will always be equal, but the only time all angles in a quadrilateral parallelogram are equal is when that shape is a rectangle.

Sometimes. For example, a rectangle has one set of four equal angles, and a parallelogram has two sets of two equal angles.

A square. Four 90 degree angles allow a quadrilateral to have equal sides.

square

A square

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Diagonally opposite pairs of angles will always be equal, but the only time all angles in a quadrilateral parallelogram are equal is when that shape is a rectangle.

Sometimes. For example, a rectangle has one set of four equal angles, and a parallelogram has two sets of two equal angles.

A square. Four 90 degree angles allow a quadrilateral to have equal sides.

square

It is a rhombus

square

A square

Yes, the opposite angles in a regular quadrilateral are equal.

There is no specific name for such a quadrilateral.

square

A rhombus is a 4 equal sided quadrilateral with equal opposite acute angles and equal opposite obtuse angles with diagonals that bisect each other at right angles.

If a quadrilateral has four equal angles, then it is also a rectangle. It can also be a square if it has equal sides as well.