Rhombus and Square

Goals Define rhombus. Discuss properties.

Define square. Discuss properties.

Use properties to determine if a quadrilateral is a parallelogram, rectangle, rhombus, square.

Properties of a Parallelogram Definition: Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.

Characteristics of a Rectangle See above Definition: All four angles are congruent Diagonals are congruent.

REVIEW!!

Rhombus - Definition

A rhombus is a parallelogram where all 4 sides are congruent.

The characteristics of parallelograms are also true for rhombus, since it is

a special type of parallelogram.

The plural of rhombus is “rhombi”

Rhombus - Diagonals

The diagonals of a rhombus are perpendicular.

What is the relationship between AC and BD?

A

B

C

D

Rhombus - Diagonals If the diagonals of a parallelogram are

perpendicular, then it is a rhombus.A

B

C

D

If AC is perpendicular to BD and ABCD is a parallelogram, then ABCD is a rhombus

Rhombus – Diagonals - Angles The diagonals of a rhombus bisect the opposite

angles.A

B

C

D

CBDABD CDBADB BACDAC BCADCA

Square - Definition A square is a parallelogram where all 4

angles are congruent and all four sides are congruent.

A square has all the same properties as a parallelogram, a rhombus, and a rectangle.

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties.Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties.Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

I’m thinking of a quadrilateral where all the sides are equal… what could it be?Rhombus or Square

I’m thinking of a quadrilateral where the opposite sides are parallel… what could it be?Para, Rect, Rhom, or Square

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties.Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties.Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Best Name??

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties.Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties.Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Best Name??

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties.Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties.Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Best Name??

Caution!There is a difference between…

What could this be? What’s the best name?

It COULD be a parallelogram or a rectangle.

All we know FOR SURE is that it is a parallelogram.

Match the property with all of the types of quadrilateral which have that property.

The diagonals are congruent.

Parallelogram

Rectangle

Rhombus

Square

Match the property with all of the types of quadrilateral which have that property.

Both pairs of opposite sides are congruent.

Parallelogram

Rectangle

Rhombus

Square

Parallelograms Both pairs opp. sides of are parallel. Both pairs opp. sides are congruent Both pairs opp. angles are congruent All consecutive angles add to 180. Diagonals bisect each other. One pair of sides is parallel and congruent.Rectangles All four angles are congruent Diagonals are congruent. ALL parallelogram properties.Rhombi All four sides are congruent Diagonals are perpendicular. Opp. angles are bisected. ALL parallelogram properties.Squares The only regular quadrilateral. ALL properties of para, rect, and rhom.

Quadrilaterals4 sides, angles add to 360

ParallelogramsOpp sides parallel, Opp sides congruent, Opp angles congruent, Consecutive

angles =180, Diagonals bisect

RectangleAll angles are congruent.Diagonals are congruent.

RhombusAll sides are congruent.Diagonals are perpendicular.Opp angles are bisected.

SquareEverything