True or False
All trapezoids are quadrilaterals.
True. All trapezoids have the defining properties of a quadrilateral plus at least one set of parallel sides.
This is the most specific name for a quadrilateral with four equal sides and four right angles.
What is a square?
Every square is also a member of this category because it has four right angles.
What is a rectangle?
Why is a square always a rectangle?
Because a square has four right angles, which is the defining attribute of a rectangle.
In this shape, the diagonals bisect each other at 90-degree angles, but they are not always equal in length.
What is a rhombus?
All parallelograms are rhombuses.
False. While some parallelograms are rhombuses, only those with four sides of equal length fit the definition of a rhombus.
This is a quadrilateral with at least one pair of opposite parallel sides.
What is a trapezoid?
This is the name given to any two-dimensional figure with four straight sides.
What is a quadrilateral?
Why is a rectangle not always a square?
A rectangle only needs four right angles; it does not need all four sides to be equal in length.
In this shape, the diagonals are always equal in length and bisect each other, but they are not necessarily perpendicular.
All rectangles are squares
False. Rectangles only require four right angles, whereas a square must also have four sides of equal length
This is a quadrilateral with two pairs of equal adjacent sides, but its opposite sides are not necessarily equal.
What is a kite?
This specific name is given to diagonals that cross each other at their exact midpoints.
What is bisect?
Explain why all rhombuses are kites.
A kite must have two pairs of equal adjacent sides; since a rhombus has four equal sides, its adjacent sides are always equal.
This quadrilateral has diagonals that are perpendicular, but only one of the diagonals is bisected.
What is a kite?
All rhombuses are squares.
False. All rhombuses have four equal sides, but only those with four right angles are squares
This is the name for a quadrilateral with two pairs of opposite parallel sides.
What is a parallelogram?
This angles fall between 90 and 180 degrees.
What is an obtuse angle?
A parallelogram is a member of this larger category because it has at least one pair of parallel sides.
Trapezoid
This quadrilateral is the most specific because its diagonals are equal, they bisect each other, AND they are perpendicular.
What is a square?
Kites are never rhombuses.
False. A kite is a rhombus if all four of its sides are equal in length.
This is the most specific name for a parallelogram that has four equal sides but not necessarily four right angles.
What is a Rhombus?
This type of trapezoid has exactly two equal sides, similar to a specific type of triangle.
What is an isosceles trapezoid?
Because attributes belonging to a category also belong to all subcategories, any property of a parallelogram must also be true for these three shapes.
Rhombuses, Rectangles, and Squares.
These are the only two types of parallelograms whose diagonals are always perpendicular bisectors of each other.
What are rhombuses and squares?