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Rhombus

Parallelogram

Normal Trapezoid properties

Isosceles Trapezoid Properties

1. Diagonals are perpendicular bisectors of each other 2. Dia…

1. diagonals bisect each other 2. Opposite angles are congrue…

1. Consecutive angles are supplementary 2. Mid segment is par…

1. Base angles are congruent 2.diagonals are congruent

Rhombus

1. Diagonals are perpendicular bisectors of each other 2. Dia…

Parallelogram

1. diagonals bisect each other 2. Opposite angles are congrue…

Addition Property

Subtraction Property

Multiplication Property

Division Property

x - 10 = 40 AB = GH... x = 50 AB + CD = GH + CD

x + 8 = 12 AB + GH = CD + GH... x = 4 AB = CD

x m<a = 90'... _ = 4 ... 5 2m<a =180'... x = 20

8x = 40 2m<b = 180'... x = 5 _ _... 2 2... m<b = 90'

Addition Property

x - 10 = 40 AB = GH... x = 50 AB + CD = GH + CD

Subtraction Property

x + 8 = 12 AB + GH = CD + GH... x = 4 AB = CD

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

if a = b, then a + c = b + c

if a = b, then a - c = b - c

if a = b, then a x c = b x c

If a = b and c does not = 0, then a/c = b/c

addition property of equality

if a = b, then a + c = b + c

subtraction property of equality

if a = b, then a - c = b - c

Parrallelogram

Parallelogram

Parallelogram

Parallelogram

Two pairs of opposite sides congruent

Two pairs of opposite angles congruent

Consecutive angles are supplementary

Diagonals bisect the interior angles

Parrallelogram

Two pairs of opposite sides congruent

Parallelogram

Two pairs of opposite angles congruent

For a reflection, you need to know:

For a translation, you need to know:

For a ritation, you need to know:

Basic Rigid Motion

Line of reflection (little r)

Vector of translation (big T)

Center of rotation, angle of rotation (big R)

...

For a reflection, you need to know:

Line of reflection (little r)

For a translation, you need to know:

Vector of translation (big T)

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then ac=bc

If a=b and c≠0, then a/c=b/c

Addition Property of Equality

If a=b, then a+c=b+c

Subtraction Property of Equality

If a=b, then a-c=b-c

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The distance between points A and B, written as AB, is the ab…

If B is between A and C, then AB + BC = AC; ... If AB + BC + AC,…

The measure of <ABC is equal to the absolute value of the dif…

If A is in the interior of <BCD, then the measure of <BCD is…

Ruler Postulate

The distance between points A and B, written as AB, is the ab…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC; ... If AB + BC + AC,…

Exactly one pair of opposite sides are…

Both pairs of opposite sides are congr…

All sides are congruent.

Both pairs of consecutive sides are co…

Isosceles Trapezoid

Parallelogram, Rectangle, Rhombus, Square

Rhombus, Square

Kite

Exactly one pair of opposite sides are…

Isosceles Trapezoid

Both pairs of opposite sides are congr…

Parallelogram, Rectangle, Rhombus, Square

Properties of a kite

properties of a trapezoid

properties of an isosceles trapezoid

midsegments of a triangle

1. The diagonals are perpendicular... 2. The diagonal connecting…

the consecutive angles between the two bases are supplementary

1. the base angles are congruent... 2.the diagonals are congruent

1. divide it into 4 congruent triangles... 2. parallel to the th…

Properties of a kite

1. The diagonals are perpendicular... 2. The diagonal connecting…

properties of a trapezoid

the consecutive angles between the two bases are supplementary

1)Rhombus

2) rhombus

3)rhombus

1) parallelogram

All sides of a rhombus are congruent equilateral

The diagonals of a rhombus are perpendicular

The diagonals bisect it's angles

A parallelogram has 2 parallel sides

1)Rhombus

All sides of a rhombus are congruent equilateral

2) rhombus

The diagonals of a rhombus are perpendicular

parallelogram, rectangle, rhombus, squ…

parallelogram, rectangle, rhombus, squ…

parallelogram, rectangle, rhombus, squ…

parallelogram, rectangle, rhombus, squ…

both pairs of opp sides are parallel

both pairs of opp sides are congruent

both pairs of opp angles are congruent

all pairs of consecutive angles are supp

parallelogram, rectangle, rhombus, squ…

both pairs of opp sides are parallel

parallelogram, rectangle, rhombus, squ…

both pairs of opp sides are congruent

reflexive property

symmetric property

transitive property

addition postulate

a quantity is congruent to itself

if a = b, then b = a

if a = b and b = c, then a = c

if equal quantities are added to equal quantities, the sums a…

reflexive property

a quantity is congruent to itself

symmetric property

if a = b, then b = a

Properties of Equality

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Let a, b, and c be real numbers

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then ac=bc

Properties of Equality

Let a, b, and c be real numbers

Addition Property of Equality

If a=b, then a+c=b+c

Addition prop. Of =

Subtraction prop. Of =

Multiplication prop. Of =

Division prop. Of =

m<A = m<B ... m<A + 30 = m<B + 30

m<A = m<B... m<A - 30 = m<B - 30

m<A = m<B... 2(m<A) = 2(m<B)

m<A = m<B... m<A/2 = m<B/2

Addition prop. Of =

m<A = m<B ... m<A + 30 = m<B + 30

Subtraction prop. Of =

m<A = m<B... m<A - 30 = m<B - 30

Addition

Subtraction

Multiplication

Division

Plain addition (both sides of the equal sign)

Plain subtraction (both sides of the equal sign)

Plain multiplication (both sides of the equal sign)

Plain division (both signs of the equal sign)

Addition

Plain addition (both sides of the equal sign)

Subtraction

Plain subtraction (both sides of the equal sign)

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with the real…

If B is between A and C, then AB+BC=AC.

The measure of ∠AOB, which can be written as m∠AOB, is equal…

If P is in the interior of ∠RST, then the measure of ∠RST is…

Ruler Postulate

The points on a line can be matched one to one with the real…

Segment Addition Postulate

If B is between A and C, then AB+BC=AC.

One pair of parallel sides

Diagonals are congruent

Opposite sides are congruent

Diagonals bisect the angles

Trapezoid, Isosceles Trapezoid

Rectangle, Square, Isosceles Trapezoid

Rhombus, Rectangle, Parallelogram, Square

Rhombus, Square

One pair of parallel sides

Trapezoid, Isosceles Trapezoid

Diagonals are congruent

Rectangle, Square, Isosceles Trapezoid

If equals are added to equals, then th…

If equals are subtracted from equals,…

If equals are multiplied by equals, th…

If equals are divided by non-zero equa…

Addition Postulate

Subtraction Property

Multiplication property

Division Property

If equals are added to equals, then th…

Addition Postulate

If equals are subtracted from equals,…

Subtraction Property

properties of parallelograms

conditions for parallelograms

properties for rectangles

conditions for rectangles

opposite sides are parallel, opposite sides are congruent, op…

if opposite sides are parallel, if one pair of opposite sides…

is a parallelogram has all the properties of parallelograms,…

if it has at least one right angle, if its diagonals are cong…

properties of parallelograms

opposite sides are parallel, opposite sides are congruent, op…

conditions for parallelograms

if opposite sides are parallel, if one pair of opposite sides…

Addition property of equality

Subtraction property of equality

Multiplication property of equality

Division property of equality

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then a•c=b•c

If a=b, then a/c= b/c

Addition property of equality

If a=b, then a+c=b+c

Subtraction property of equality

If a=b, then a-c=b-c

opposite sides are parallel

opposite sides are congruent

opposite angles are congruent

a diagonal forms two congruent angles

ALL: rectangle, rhombus, parallelogram, square

ALL: rectangle, rhombus, parallelogram, square

ALL: rectangle, rhombus, parallelogram, square

ALL: rectangle, rhombus, parallelogram, square

opposite sides are parallel

ALL: rectangle, rhombus, parallelogram, square

opposite sides are congruent

ALL: rectangle, rhombus, parallelogram, square

What are polygons?

What are quadrilaterals?

What is the family tree?

How many properties does a p'gram have?

Closed figure with straight sides

A shape with 4 sides and 4 angles

Quads, p'gram, rectangle, rhombus, square

5

What are polygons?

Closed figure with straight sides

What are quadrilaterals?

A shape with 4 sides and 4 angles

Quadrilateral

Parallelogram

Rectangle

Rhombus

angle sum is 360 and 4 sides

diagonals bisect each other, opposite sides parallel, opposit…

Diagonals congruent, and equiangular

equilateral, diagonals are perpendicular, diagonals bisect th…

Quadrilateral

angle sum is 360 and 4 sides

Parallelogram

diagonals bisect each other, opposite sides parallel, opposit…

One pair of opposite angles equal

one pair of opposite sides equal

one pair of parallel sides

both pair of opposite sides equal

kite

isos trapezoid

trapezoid & isos trapezoid

Parallelogram, rhombus, square & rectangle

One pair of opposite angles equal

kite

one pair of opposite sides equal

isos trapezoid

Opposite side are parallel

Opposite sides and angles are congruen…

Consecutive angles are supplements

All angles are congruent

Parallelogram... Rectangle... Rhombus... Square ... Kite

Parallelogram ... Rectangle... Rhombus ... Square

Parallelogram ... Rectangle ... Rhombus ... Square

Rectangle ... Square

Opposite side are parallel

Parallelogram... Rectangle... Rhombus... Square ... Kite

Opposite sides and angles are congruen…

Parallelogram ... Rectangle... Rhombus ... Square

Addition Property

Subtraction Property

Multiplication Property

Division Property

If a = b, then a + c = b + c

If a = b, then a - c = b - c

If a = b then ac = bc

If a = b then c does not equal 0 then a/c = b/c

Addition Property

If a = b, then a + c = b + c

Subtraction Property

If a = b, then a - c = b - c

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If equals are added to equals, the results are equal: If a=b,…

If equals are subtracted from equals, the results are equal:…

If equals are multiplied by equals, their products are equal:…

If equals are divided by nonzero equals, their quotients are…

Addition Property of Equality

If equals are added to equals, the results are equal: If a=b,…

Subtraction Property of Equality

If equals are subtracted from equals, the results are equal:…

If it is a parallelogram it is also wh…

If it is a rectangle it is also what?

If it is a rhombus it is also what?

Properties of a parallelogram

Rectangle, rhombus, and square

A square

A square

1. Both pairs of opposite sides are congruent ... 2. Both pairs…

If it is a parallelogram it is also wh…

Rectangle, rhombus, and square

If it is a rectangle it is also what?

A square

Centroid

Midpoint

Midpoint Line

Circumcenter

Three lines from three midpoints intersecting.

The middle point of a line segment.

A line coming from the midpoint.

The intersection of three perpendicular bisectors.

Centroid

Three lines from three midpoints intersecting.

Midpoint

The middle point of a line segment.

circle

radius

chord

diameter

the set of all points in a plane that are equidistant from a…

a segment whose endpoints are the center of a circle and any…

a segment whose endpoints are on a circle

a chord that contains the center of the circle

circle

the set of all points in a plane that are equidistant from a…

radius

a segment whose endpoints are the center of a circle and any…

Which shapes have exactly one pair of…

Which shapes have both pairs of opposi…

Which shape has exactly one pair of op…

Which shapes have both pairs of opposi…

Trapezoid and isosceles trapezoid

llogram, rectangle, rhombus, square (PRRS)

Isosceles trapezoid

llogram, rectangle, thrombus, square (PRRS)

Which shapes have exactly one pair of…

Trapezoid and isosceles trapezoid

Which shapes have both pairs of opposi…

llogram, rectangle, rhombus, square (PRRS)