Geometry: Quadrilaterals and Their Properties

Vocabulary flashcards defining geometric terms, properties, conditions, and relationships for quadrilaterals based on lecture notes.

Quadrilateral

A simple closed polygon with four sides, four vertices, and four angles.

Trapezium

A quadrilateral with no pairs of parallel sides.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Bases of a trapezoid

The pair of parallel sides of a trapezoid.

Legs of a trapezoid

The non-parallel sides of a trapezoid.

Isosceles trapezoid

A trapezoid whose non-parallel sides (legs) are congruent.

Parallelogram

A quadrilateral with two pairs of opposite parallel sides.

Rectangle

A parallelogram with four right angles.

Rhombus

A parallelogram with four congruent sides.

Square

A quadrilateral with four congruent sides and four right angles; it is both a rectangle and a rhombus.

Kite

A quadrilateral with two distinct pairs of adjacent congruent sides.

Congruent sides

Sides that have the same length.

Right angle

An angle measuring exactly $90$ degrees.

Opposite sides of a parallelogram

They are parallel and congruent.

Opposite angles of a parallelogram

They are congruent.

Consecutive angles of a parallelogram

They are supplementary; their measures add up to $180$ degrees.

Diagonals of a parallelogram

They bisect each other.

Condition 1 for a parallelogram

A pair of opposite sides can be both parallel and congruent.

Condition for a parallelogram (Opposite Sides)

Both pairs of opposite sides are congruent.

Condition for a parallelogram (Diagonals)

The diagonals bisect each other.

Condition for a parallelogram (Opposite Angles)

Opposite angles are congruent.

Relationship between square and rectangle

Every square is a rectangle because it has four right angles.

Relationship between square and rhombus

Every square is a rhombus because it has four congruent sides.

Relationship between rectangle and square

Not every rectangle is a square; a rectangle only needs four right angles.

Relationship between rhombus and square

Not every rhombus is a square; a rhombus only needs four congruent sides.

Main classification of quadrilaterals

Trapezium: no pairs; trapezoid: one pair; parallelogram: two pairs of opposite parallel sides.

How to identify a quadrilateral

Check that the figure is a closed polygon made of four line segments.

How to identify a rectangle

Look for a parallelogram with four right angles.

How to identify a rhombus

Look for a parallelogram with four congruent sides.

How to identify a square

Look for four congruent sides and four right angles.

How to identify a kite

Look for two distinct pairs of adjacent congruent sides.

How to identify an isosceles trapezoid

Look for a trapezoid whose non-parallel sides are congruent.