Classifying Quadrilaterals 5th Grade Geometry true or false

Every quadrilateral has parallel sides.

False - A quadrilateral is a polygon with 4 sides. They do not have to be parallel to be a quadrilateral.

Every quadrilateral has perpendicular sides.

False - A quadrilateral is a polygon with 4 sides. They do not have to be perpendicular (right angles or 90 degree angle)

Every rhombus is a rectangle.

False - A rectangle must always have 4 right angles (90 degree angles). All rhombuses or rhombi do not have to have 4 right angles. Their opposite angles must be equal to each other, however, because they're parallelograms.

Every parallelogram is a rectangle.

False - All rectangles are parallelograms because both pairs of opposite sides are parallel and equal in length. However, not all parallelograms have 4 right angles. In order for it to be called a rectangle, it must also have 4 right angles.

Every rhombus has perpendicular sides.

False - Some rhombus have perpendicular sides, but not all. If a rhombus has perpendicular sides (right angles) it can also be called a square.

Every trapezoid has perpendicular sides.

False - Some trapezoids may have one or two right angles (perpendicular sides), but every trapezoid does not have perpendicular sides.

Every rhombus is a square.

False - The definition of a rhombus is a parallelogram with all sides the same length. While a rhombus and square both have sides equal in length, the angles of a rhombus are not always right angles (90 degrees) as they are with a square. However, every square is a rhombus because all sides are the same length.

Every trapezoid is a parallelogram.

False - Trapezoids only have one pair of parallel sides. Parallelograms must have both pairs of opposite sides equal and parallel.

Every rhombus has four right angles.

False. All rhombuses must have 4 equal sides, but their angles are not always right angles. If it is a square, then it is a rhombus with 4 right angles.

Every rectangle is a parallelogram.

True - A parallelogram has both pairs of opposite sides parallel and equal in length. A rectangle is a parallelogram with 4 right angles.

Every trapezoid is a quadrilateral.

True - A quadrilateral has 4 sides. Trapezoids have 4 sides.

Every square has four right angles.

True - A square is a rectangle with all sides the same length. All rectangles have 4 right angles. A square is a quadrilateral, parallelogram, rectangle, and rhombus.

Every rectangle has perpendicular sides.

True - All rectangles have 4 right angles (90 degrees). Right angles form perpendicular lines.

Every square has perpendicular sides.

True - Every square is also a rectangle. The definition of a rectangle is a parallelogram with 4 right angles. Right angles form perpendicular lines.

Every rhombus is a parallelogram.

True - The definition of a parallelogram says that both pairs of sides are parallel and equal in length. A rhombus is a special type of parallelogram with opposite sides parallel, and all sides equal in length.

Every square is a rectangle.

True - The definition of a rectangle is it's a parallelogram with 4 right angles. All squares are rectangles because all squares have 4 right angles.

Every square is a rhombus.

True - The definition of a rhombus states that all sides are the same length. A square is a special type of rhombus because it has all sides the same length and 4 right angles. A square has many names. It can be called a rhombus, a rectangle, a parallelogram, and a quadrilateral. However, the opposite is not always true. For example, all quadrilaterals are not squares. All parallelograms are not squares. All rectangles are not squares. All rhombi (rhombuses) are not squares.

Every trapezoid has parallel sides.

True - Trapezoids have one pair of parallel sides.

Every rectangle is a square.

false - Squares are considered rectangles because they have 4 right angles, but all rectangles are not squares because to be a square a quadrilateral must also have 4 equal sides or line segments in addition to 4 right angles.