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Parallelogram

Rhombus

Rectangle

Square

Parallelogram

Rhombus

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

Parallelogram

Rectangle

Kite

Rhombus

1.) Opposite sides are parallel... 2.) Opposite sides are congru…

0.) Rectangle is a parallelogram (#1-5)... 1.) Opposite sides ar…

1.) Two disjoint pairs of consecutive sides are congruent ... 2.…

0.) Rhombus is a parallelogram (#1-5)... 1.) Opposite sides are…

Parallelogram

1.) Opposite sides are parallel... 2.) Opposite sides are congru…

Rectangle

0.) Rectangle is a parallelogram (#1-5)... 1.) Opposite sides ar…

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

if a=b and c=d the a+c=b+d

if a=b and c=d then a-c=b-d

if a=b then ca=cb

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

addition property of equality

if a=b and c=d the a+c=b+d

subtraction property of equality

if a=b and c=d then a-c=b-d

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b and c=d, then a+c=b+d. If the same amount is added to…

If a=b and c=d, then a-c=b-d. When both sides of an equation…

If a=b, then ca=cb. If you multiply both sides of an equation…

If a=b and c=0, then a/c=b/c. You can divide both sides of th…

Addition Property of Equality

If a=b and c=d, then a+c=b+d. If the same amount is added to…

Subtraction Property of Equality

If a=b and c=d, then a-c=b-d. When both sides of an equation…

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a + b = b+a

ab = ba

(a + b) + c = a + (b + c)

(ab)c = a(bc)

commutative property of addition

a + b = b+a

commutative property of multiplication

ab = ba

Reflexive Property

Symmetric Property

Transitive Property

Addition Postulate

A quantity is congruent to itself, a=a

If b=a then a=b

If a=b and b=c then a=c

If equal quantities are added to equal quantities, then the s…

Reflexive Property

A quantity is congruent to itself, a=a

Symmetric Property

If b=a then a=b

Kite

Trapezoid

Isosceles Trapezoid

Parallelogram

1. Diagonals are perpendicular... 2. Two pairs of consecutive co…

1. Only one pair of parallel sides... 2. Leg angles are suppleme…

1. Only one pair of parallel sides... 2. Leg angles are suppleme…

1. Consecutive angles are supplementary... 2. Opposite angles ar…

Kite

1. Diagonals are perpendicular... 2. Two pairs of consecutive co…

Trapezoid

1. Only one pair of parallel sides... 2. Leg angles are suppleme…

two pairs of opposite sides are parallel

only one pair of opposite sides are pa…

two pairs of opposite sides are congru…

two pairs of consecutive sides are con…

parallelogram, rectangle, rhombus, square

trapezoid, isosceles trapezoid

parallelogram, rectangle, rhombus, square

kite (by definition)

two pairs of opposite sides are parallel

parallelogram, rectangle, rhombus, square

only one pair of opposite sides are pa…

trapezoid, isosceles trapezoid

addition property

subtraction property

multiplication property

division property

property that states that if a=b, then a+c=b+c

property that states that if a=b, then a-c=b-c

property that states that if a=b, then ac=bc

property that states that if a=b and c does not equal 0, then…

addition property

property that states that if a=b, then a+c=b+c

subtraction property

property that states that if a=b, then a-c=b-c

Quadrilateral Definition

Parallelogram Definition

Rectangle Definition

Rhombus Definition

A four-sided polygon

A quadrilateral in which both pairs of opposite sides are par…

A parallelogram in which at least one angle is a right angle

A parallelogram in which at least two consecutive sides are c…

Quadrilateral Definition

A four-sided polygon

Parallelogram Definition

A quadrilateral in which both pairs of opposite sides are par…

Communative Property of Addition

Communative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

A + b = b + a

Ab = ba

(A + b) + c = a + (b + c)

(Ab)c = a(bc)

Communative Property of Addition

A + b = b + a

Communative Property of Multiplication

Ab = ba

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

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

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

If a=b, then ca=cb

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

Addition Property of Equality

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

Subtraction Property of Equality

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

Parallelogram

Kite

Trapezoid

Rhombus

Definition: both pairs of opposite sides are parallel... Propert…

Definition: two distinct pairs of consecutive sides congruent…

Definition: bases are parallel

Definition: Parallelogram and one pair of consecutive sides c…

Parallelogram

Definition: both pairs of opposite sides are parallel... Propert…

Kite

Definition: two distinct pairs of consecutive sides congruent…

commutative property of addition

associative property of addition

commutative property of multiplication

associative property of multiplication

a + b = b + a

(a + b) + c = a + (b + c)

a x b = b x a

(a b) c = a (b c)

commutative property of addition

a + b = b + a

associative property of addition

(a + b) + c = a + (b + c)

Quadrilateral

Parallelogram

Rectangle

Square

A polygon with four sides

opposite sides congruent... opposite angles congruent... consecutiv…

interior angles are 90 degrees... diagonals are congruent

interior angles are 90 degrees... diagonals are congruent... all si…

Quadrilateral

A polygon with four sides

Parallelogram

opposite sides congruent... opposite angles congruent... consecutiv…

transitive property

substitution property

subtraction property

addition property

if A=B and B=C, then A=C

if A=B then B can replace A in any expression

if 2 congruent angles/segments were subtracted from congruent…

if congruent angles/segments are added to congruent angles/se…

transitive property

if A=B and B=C, then A=C

substitution property

if A=B then B can replace A in any expression

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

The diagonals bisect each other

The diagonals are congruent

Each diagonal bisects an opposite pair…

The diagonals are perpendicular

Parallelogram, Rectangle, Rhombus, Square

Isos. Trapezoid, Rectangle, Square

Rhombus, Square

Rhombus, Square, Kite

The diagonals bisect each other

Parallelogram, Rectangle, Rhombus, Square

The diagonals are congruent

Isos. Trapezoid, Rectangle, Square

commutative property of addition

associative property of addition

commutative property of multiplication

associative property of multiplication

a + b = b + a

(a + b) + c = a + (b + c)

a x b = b x a

(a b) c = a (b c)

commutative property of addition

a + b = b + a

associative property of addition

(a + b) + c = a + (b + c)

Parallelogram

Rectangle

Square

Rhombus

1)Both pairs of opp. sides parallel... 2)Both pairs opp. sides c…

1)All 4 angles congruent (90, rt angles)... 2)Diagonals congruen…

1)All properties of Parall., rect. and rhombus... 2)All sides an…

1)All properties of Parallelogram... 2)All sides congruent... 3)Dia…

Parallelogram

1)Both pairs of opp. sides parallel... 2)Both pairs opp. sides c…

Rectangle

1)All 4 angles congruent (90, rt angles)... 2)Diagonals congruen…

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

is a=b, then a**c = b**c

if a=b and c (doesn't) = 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

The "Three Possibilities" Property

The Transitive Property

The Addition property

Subtraction Property

Either a>b, a=b, or a<b

If a>b and b>c, then a>c

If a>b, then a+c>b+c

If a>b, then a-c>a-b

The "Three Possibilities" Property

Either a>b, a=b, or a<b

The Transitive Property

If a>b and b>c, then a>c

circle

equation of a circle (in standard form)

radius

properties of a radius

the set of all points equidistant to a point, called the center

(x-h)²+(y-k)²=r²

segment that connects the center of the circle to a point on…

all radii of a circle are congruent ... radius = ½(diameter)

circle

the set of all points equidistant to a point, called the center

equation of a circle (in standard form)

(x-h)²+(y-k)²=r²

Addition Property

Subtraction Property

Multiplication Property

Division Property

If a=b, then a+c = b+c... Ex: x-4=8; x = 12

If a=b, then a-c = b-c... Ex: x+3 = 6; x=3

If a = b, then a**b = b**c... Ex: x/3 = 2; x = 6

If a = b and c=0, then a/c = b/c... Ex: 5x = 40; x = 8

Addition Property

If a=b, then a+c = b+c... Ex: x-4=8; x = 12

Subtraction Property

If a=b, then a-c = b-c... Ex: x+3 = 6; x=3

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 and c does not = 0, then a over c = b over c

Addition property

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

Subtraction property

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

All properties of parallelograms apply…

Properties of Rhombuses, and Rectangle…

Properties of rhombuses also apply to…

Properties: Opposite sides are paralle…

True

True

False

PA

All properties of parallelograms apply…

True

Properties of Rhombuses, and Rectangle…

True

prove parallelogram

prove rhombus

prove rectangle

prove trapezoid

1) 2 pairs of opposite parallel sides... 2) 2 pairs of opposite…

1) equilateral quadrilateral... 2) a parallelogram who's diagona…

1) equiangular quadrilateral... 2) parallelogram with 1 right an…

1) quadrilateral with exactly one pair of parallel sides

prove parallelogram

1) 2 pairs of opposite parallel sides... 2) 2 pairs of opposite…

prove rhombus

1) equilateral quadrilateral... 2) a parallelogram who's diagona…

through any two points, there is exact…

through any three non-collinear points…

A line contains __

If two points lie in a plane, ___

line

plane

two or more points

the entire line containing those points lies in that plane

through any two points, there is exact…

line

through any three non-collinear points…

plane

Reflexive Property

Symmetric Property

Transitive Property

Addition Property

a=a... AB=AB... <A=<A

If a=b, then b=a.... If AB=CD, then CD=AB.

If a=b and b=c, then a=c. ... If AB=CD and CD=EF, then AB=EF.

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

Reflexive Property

a=a... AB=AB... <A=<A

Symmetric Property

If a=b, then b=a.... If AB=CD, then CD=AB.

adjacent angles

complementary angles

supplementary angles

linear pair

two coplanar angles that have a common side and a common vert…

two angles in which the sum of their measures is 90

two angles in which the sum of their measures is 180

a pair of adjacent, supplementary angles

adjacent angles

two coplanar angles that have a common side and a common vert…

complementary angles

two angles in which the sum of their measures is 90

If two angles are right angles, then t…

If two angles are straight angles, the…

If angles or segments are congruent to…

If angles or segments are congruent to…

Theorem

Theorem

Theorem

Theorem

If two angles are right angles, then t…

Theorem

If two angles are straight angles, the…

Theorem

Addition Property

Subtraction Property

Multiplication Preoperty

Division Property

Used when you add a segment or angle

Used when you subtract a segment or angle

Very rarely used (used for proving two segments or angles wou…

Used for bisections (proving two angles that were bisected or…

Addition Property

Used when you add a segment or angle

Subtraction Property

Used when you subtract a segment or angle

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 times c = b times c

if a=b and "c" does not equal 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

Addition Property of Equality

subtraction Property of equality

multiplication property of equality

division property of equality

if a=b and c=d, the a+c = b+d

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

if a=b, then ca=cb

if a=b and c is not 0 then a÷ c = b÷ c

Addition Property of Equality

if a=b and c=d, the a+c = b+d

subtraction Property of equality

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

Midpoint theorem

Addition property of =

Subtraction property of =

Multiplication property of =

If M is the midpoint of segment AB, then segment AM ≅ MB.

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

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

If a=b, then a x c = b x c.

Midpoint theorem

If M is the midpoint of segment AB, then segment AM ≅ MB.

Addition property of =

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

acute angle

angle bisector

collinear

coplanar

an angle who's measure is between 0 and 90

a ray that divides an angle into two congruent angles

three or more points that lie on the same line

figures in the same plane

acute angle

an angle who's measure is between 0 and 90

angle bisector

a ray that divides an angle into two congruent angles

Both pairs of opposite sides are //

Both (All) pairs of opposite sides are…

Both (ALL) pairs of opposite angles ar…

ALL pairs of consecutive angles are su…

Parallelogram, Rhombus, Rectangle Square (PRSR)

Parallelogram, Rhombus Rectangle Square (PRSR)

Parallelogram, Rhombus, Rectangle, Square (PRSR)

Parallelogram, Rhombus, Rectangle, Square (PRSR)

Both pairs of opposite sides are //

Parallelogram, Rhombus, Rectangle Square (PRSR)

Both (All) pairs of opposite sides are…

Parallelogram, Rhombus Rectangle Square (PRSR)

Symmetric Property of Equality

Multiplication Property of Equality

Reflexive Property of Congruence

Reflexive Property of Equality

If a=b, then b=a

If a=b, then ac=bc

AB is congruent to AB

a=a

Symmetric Property of Equality

If a=b, then b=a

Multiplication Property of Equality

If a=b, then ac=bc

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 a(c)= b(c).

If a=b and c doesn't equal 0, then a divided by c = b divided…

Addition Property

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

Subtraction Property

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

Parallelogram

Quadrilateral

Theorem 1

Theorem 2

a quadrilateral with both pairs of opposite sides parallel

Polygon with four sides; sum of measures = 360 degrees

Opposite sides of a parallelogram are congruent

The opposite angles of a parallelogram are congruent

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

Quadrilateral

Polygon with four sides; sum of measures = 360 degrees