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What quadrilateral has four congruent sides but its diagonals are not congruent?
Rhombus.
What describes a rhombus?
A rhombus is a parallelogram with all 4 sides congruent. The diagonals bisect(split in have) the interior angles. The diagonals are perpendicular to each other.
Are diagonals congruent if they bisect each other?
Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.
What is a description of a parallelogram?
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???
What are four attributes of a rhombus?
1. Opposite angles congruent 2. All sides are congruent 3. The diagonals are perpendicular bisectors of each other 4. Diagonals bisect the angles NOTE: Four congruent right triangles are formed with the right angles It has all of the properties of a parallelogram and a kite
