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Q: A parallelogram with four right angles and opposite sides congruent?

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Yes. A parallelogram is effectively a rectangle that doesn't have right angles.

It can also be a kite. That has two congruent pairs of sides but unlike a parallelogram they are adjacent, not opposite. A parallelogram with congruent diagonals is a rectangle.

If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Opposite angles are congruent. Opposite sides are congruent. Consecutive angles are supplementary.

A parallelogram with no right angles and four congruent sides is a Rhombus.

Yes. This is true because opposite angles are congruent and adjacent angles are supplementary.

A rhombus is a parallelogram with all four sides congruent to each other with no right angles. A square is a parallelogram with four congruent sides and four right angles.

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A square has 4 congruent sides and 4 right angles, in addition to having all of the properties of a parallelogram. A kite is not a parallelogram. It has two pairs of consecutive congruent sides, and a pair of congruent opposite angles.

This is a parallelogram, opposite sides are of equal length and opposite angles are equal in size.

A rhombus (4 congruent sides, diagonals perpendicular)that is not also a square (no right angles), andis also a parallelogram (opposite sides parallel and congruent, opposite angles congruent). It is also a quadrilateral, which has 4 sides.

A parallelogram is a quadrilateral (4-sided figure) with both pairs of opposite sides parallel. That's usually the primary definition. There are properties common to all parallelograms: opposite sides are congruent, opposite angles are congruent, and diagonals bisect each other. Other special parallelograms have additional properties. A rectangle is a parallelogram with four right angles and its diagonals are congruent. A rhombus is a parallelogram with four congruent sides. Its diagonals are perpendicular and each diagonal bisects two angles of the rhombus. A square is a parallelogram as well. It has four right angles and four congruent sides, so it is also a rectangle and a rhombus. How's that for confusing???

No. If the diagonals of a parallelogram are congruent then it must be a rectangle (or square).

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