Properties of Quadrilaterals

Properties of Quadrilaterals

Quadrilaterals Defined

• A polygon with 4 sides

• All sides are straight

Types of quadrilaterals

• parallelogram

• rectangle

• square

• rhombus

• trapezoid

• isosceles trapezoid

• kite

Parallelogram properties

• opposite sides are parallel (2 pairs)

• diagonals bisect each other

• diagonals are not congruent

Parallelogram Properties

• opposite angles are congruent

• opposite sides are congruent

• Consecutive angles are supplementary

Multiple Choice

Which is NOT a property of a parallelogram?

• Diagonals bisect each other

• Diagonals are congruent

• Both pairs of opposite sides are parallel

• Both pairs of opposite angles are congruent

Properties of Rectangles

• ALL angles are right angles

• opposite sides are congruent

Properties of Rectangles

• diagonals bisect each other

• diagonals are congruent

Multiple Select

Which of the following is true about the diagonals of a rectangle? Select all that are true.

• Diagonals bisect each other

• Diagonals are congruent

• Diagonal are perpendicular

• Diagonals bisect the angles

Properties of a Rhombus

• ALL 4 sides are congruent

• opposite angles are congruent

• diagonals bisect each other and opposite angles too

• diagonals are perpendicular

• diagonals are NOT congruent

• consecutive angles are supplementary

• a rhombus is a parallelogram

Multiple Choice

Which of the following are NOT true about diagonals of a rhombus?

• they are perpendicular

• they bisect each other

• they are congruent

Properties of Squares

• All 4 sides are congruent

• All 4 angles are right angles

• the diagonals bisect each other

• the diagonals are congruent

• The diagonals are perpendicular

• the diagonals bisect the angles of the square

Multiple Choice

The diagonals of a square are

• parallel

• congruent

• perpendicular

• congruent and perpendicular

Properties of a Trapezoid

• 1 pair of parallel sides

• parallel sides are called bases

• "non-parallel" sides are called legs

• diagonals have no particular distinction.

• ALL 4 angles have different angle measures.

Properties of an Isosceles Trapezoid

• same properties as a "trapezoid"....except:

• the legs are congruent

• 2 pairs of congruent base angles

• diagonals are congruent

Multiple Choice

The diagonals of a trapezoid bisect each other.

• True

• False

Multiple Choice

The legs of an isosceles trapezoid are _____.

• parallel

• perpendicular

• congruent

• skew

Properties of a Kite

• 2 pairs of adjacent sides are congruent

• 1 pair of opposite angles are congruent

• 1 diagonal is bisected

• diagonals are NOT congruent

• diagonals are perpendicular

Multiple Choice

In the kite JKLM, segment KM is perpendicular to segment _____.

• JM

• KL

• JL

• LM

Multiple Choice

A rectangle is also a _____________

• square
• parallelogram
• rhombus
• it is just a rectangle

Multiple Choice

The diagonals of a ________ are congruent

• Parallelogram
• Rectangle and square
• Rhombus and square
• Trapezoid

Multiple Choice

A rhombus has all of the properties of a 

• Parallelogram
• Trapezoid
• Kite
• Square

Multiple Choice

Which statement is FALSE? 
A parallelogram _____________

• Has 2 sets of parallel sides
• Has diagonals that are perpendicular
• Has diagonals that bisect each other

Multiple Choice

Which quadrilateral is also considered a rhombus, rectangle, and parallelogram?

• Trapezoid
• Triangle
• Square
• Hexagon

Multiple Choice

Classify the quadrilateral in as many ways as possible.

• quadrilateral, parallelogram
• rectangle
• quadrilateral,parallelogram, rectangle
• quadrilateral,parallelogram, rectangle, square

Multiple Choice

Which conclusion can be drawn?

• All quadrilaterals are kites, but all kites are not quadrilaterals.

• All parallelograms are rhombi, but all rhombi are not parallelograms.

• All squares are parallelograms, but all parallelograms are not squares.

• All parallelograms are rectangles, but all rectangles are not parallelograms.

Multiple Choice

Which describes a rhombus?

• has all right angles

• has all acute angles

• has all equal sides

• has all obtuse angles

Multiple Choice

Colton drew a parallelogram with four sides of equal length and two pairs of equal angles. What shape did he draw?

• kite

• rectangle

• square

• trapezoid

Multiple Choice

Brayden is working on a report in which he will compare and contrast the different types of quadrilaterals. Which statement should NOT be included in his report?

• All rhombuses are squares.

• All squares are parallelograms.

• All squares and rectangles have opposite sides that are congruent.

• All parallelograms, rectangles, and squares have opposite angles that are congruent.

Multiple Choice

Which quadrilateral is also considered a rhombus, rectangle, and parallelogram?

• Trapezoid
• Triangle
• Square
• Hexagon

Multiple Choice

Classify this quadrilateral in as many ways as possible.

• quadrilateral, parallelogram
• quadrilateral, rhombus, paralleogram
• quadrilateral, paralellogram, rectangle
• quadrilateral, parallelogram, trapezoid

Multiple Choice

Classify this quadrilateral in as many ways as possible.

• quadrilateral, parallelogram, rhombus, square
• quadrilateral, parallelogram
• quadrilateral, rhombus
• quadrilateral, parallelogram, rhombus

Summary

• Squares are rectangles, rhombi, kites, and parallelograms.

• Rectangles and rhombi are parallelograms.

• Rhombi are also kites.

• Note: Some people consider parallelograms to be trapezoids.