A quadrilateral with equal adjacent angles is called a rectangle. In a rectangle, each angle measures 90 degrees, and adjacent angles are equal. This property distinguishes rectangles from other quadrilaterals, such as rhombuses or parallelograms, where angles may not be right angles.
A quadrilateral with four sides of equal length is called a rhombus. In addition to having equal side lengths, a rhombus also has opposite angles that are equal and adjacent angles that are supplementary. If all angles are right angles, it is specifically a square, which is a special type of rhombus.
A Quadrilateral Kite!
If a set of equal sides are adjacent, then the quadrilateral is a "kite" shape. If a set of equal sides are opposite, then the quadrilateral is a parallelogram.
The interior angles of a rhombus equal 180 degrees because a rhombus is a type of quadrilateral, and the sum of the interior angles of any quadrilateral is always 360 degrees. In a rhombus, opposite angles are equal, and adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, if you take any two adjacent angles in a rhombus, their sum will always equal 180 degrees.
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
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A quadrilateral with four sides of equal length is called a rhombus. In addition to having equal side lengths, a rhombus also has opposite angles that are equal and adjacent angles that are supplementary. If all angles are right angles, it is specifically a square, which is a special type of rhombus.
All quadrilaterals apart from rectangles. Even parallelograms have adjacent angles that are not equal.
A kite is a quadrilateral with two pairs of adjacent congruent sides. The angles between the unequal sides are equal.
A Quadrilateral Kite!
It's impossible for a quadrilateral to have no equal sides and have right angles.
If a set of equal sides are adjacent, then the quadrilateral is a "kite" shape. If a set of equal sides are opposite, then the quadrilateral is a parallelogram.
The interior angles of a rhombus equal 180 degrees because a rhombus is a type of quadrilateral, and the sum of the interior angles of any quadrilateral is always 360 degrees. In a rhombus, opposite angles are equal, and adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, if you take any two adjacent angles in a rhombus, their sum will always equal 180 degrees.
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
A General Quadrilateral
A rhombus is a parallelogram with all its sides equal in length but none of its internal angles are right angles. If both pairs of opposite sides are of equal but different lengths then the quadrilateral is a simple parallelogram.If the two pairs of adjacent sides are of equal but different lengths then the shape is called a kite.
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