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Geometry
Geometry quadrilaterals
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Gravity
Terms in this set (90)
Figure made of coplanar segments called sides which intersect at points called verticies
Polygon
four sided polygon
quadrilateral
a polygon with all congruent side and all congruent angles
regular polygon
(n-2) 180
sum of interior angles of a polygon
360
sum of exterior angles of a polygon
If the measure of one interior angle of a regular polygon is 144 degrees, find the number of sides
((n-2) 180)/2=144
360/36=10
Interior=144
Exterior=36
If the measure of one interior angle of a regular polygon is 160 degrees, find the number of sides.
360/20=18
Interior=160
Exterior=20
1. Both opposite sides are parallel-definition
2. Both opposite side are congruent
3. Both opposite angles are congruent
4. same sides angles are supplementary
5. Diagonals bisect each other
Parrallelogram Characteristics
If both pairs of opposite sides of a quadrilateral are parallel, then
the quadrilateral is a parallelogram
If both pairs of opposite sides of a quadrilateral are congruent, then
the quadrilateral is a parallelogram
If both pairs of opposite angles of a quadrilateral are congruent, then
the quadrilateral is a parallelogram
If both pairs of same-side angles of a quadrilateral are supplementary, then
the quadrilateral is a parallelogram
If the diagonals of a quadrilateral bisect each other, then...
the quadrilateral is a parallelogram
If one pair of opposites sides of a quadrilateral is both congruent and parallel, then...
the quadrilateral is a parallelogram
In a parallelogram, opposite sides are ____ and ____
parallel and congruent
In a parallelogram, consecutive angles are ______
Supplementary
In a parallelogram, diagonals ____ each other, which means they split each other in ____
bisect, half
1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are supplementary.
4. Same-side angles are supplementary.
5. The diagonals bisect each other.
6. All angles 90 degrees/right/congruent
7. Diagonals are congruent
Rectangle Characteristics
1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are supplementary.
4. Same-side angles are supplementary.
5. The diagonals bisect each other.
6. All sides are congruent
7. Diagonals perpendicular
8. Diagonals bisect opposite angles
Rhombus Characteristics
A square has all of the characteristics of a _____, _____, and a _______ (10 characteristics)
parallelogram, rectangle, and rhombus
Parallelogram to rectangle, rhombus to square
Parallelogram Family Tree
1 set of opposite sides parallel
Trapezoid Characteristics
1. 1 set of opposite sides parallel
2. Legs congruent (non parallel sides)
3. Base angles are congruent
4. Diagonals are congruent
Isosceles Trapezoid Characteristics
Median or midsegment will be ____ to the bases
parallel
b=1/2(a+c)
Formula for midsegment
1. Adjacent sides are congruent
2. Diagonals are perpendicular
3. 1 set of opposite angles are congruent
4. 1 set of non congruent opposite angles bisect
5. 1 diagonal bisects the other
Kite Characteristics
Parallelograms diagonals are _______ congruent
sometimes
Rectangle diagonals are ___ congruent
always
Rhombus diagonals are ___ congruent
sometimes
Square diagonals are ___ congruent
always
Trapezoid diagonals are ___ congruent
sometimes
Isosceles trapezoid diagonals are ___ congruent
always
Kite diagonals are ___ congruent
never
Parallelogram diagonals are _____ perpendicular
sometimes
Rectangle diagonals are _____ perpendicular
sometimes
Rhombus diagonals are _____ perpendicular
always
Square diagonals are _____ perpendicular
always
Trapezoid diagonals are _____ perpendicular
never
Isosceles Trapezoid diagonals are _____ perpendicular
never
Kite diagonals are _____ perpendicular
always
Parallelogram diagonals _____ bisect each other
Always
Rectangle diagonals _____ bisect each other
always
Rhombus diagonals _____ bisect each other
always
Square diagonals _____ bisect each other
always
Trapezoid diagonals _____ bisect each other
never
Isosceles trapezoid diagonals _____ bisect each other
never
A kite has only one ______ and one ______
diagonal, angle
Parallelogram diagonals ____ bisect angles
sometimes
Rectangle diagonals ____ bisect angles
sometimes
Rhombus diagonals ____ bisect angles
Always
Square diagonals ____ bisect angles
always
Trapezoid diagonals ____ bisect angles
never
Isosceles Trapezoid diagonals ____ bisect angles
never
A _____, ____, and ______ have all of the properties of a parallelogram
rectangle, rhombus, square
A ____ and ____ are equiangular (4 right corner angles)
rectangle, square
A ____ is not equiangular (4 right corner angles)
rhombus
A _____ and ___ are equilateral (4 congruent sides)
rhombus, square
A ____ is not equilateral (4 congruent sides)
rectangle
A ____ and ____ have diagonals that bisect angles
Rhombus, square
A ___ does not have diagonals that bisect angles
rectangle
A ___ and ___ have congruent diagonals
rectangle, square
A ___ does not have congruent diagonals
rhombus
A ___ and ___ have perpendicular diagonals
Rhombus, square
A ___ does not have perpendicular diagonals
rectangle
A _________'s sum of angles is 360
Quadrilaterals
A ____ has two pairs of parrallel sides
parallelogram
A ___ and ____has one pair of parallel sides
Trapezoid and isosceles trapezoid
A ___ has two congruent legs
Isosceles trapezoid
A ___ has no parallel sides and 2 pairs of consecutive side congruent
Kite
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a _____
rhombus
If one diagonal bisects a pair of opposite angles, then the parallelogram is a _____
rhombus
If the diagonals of a parallelogram are congruent, then the parallelogram is a ______
rectangle
A parallelogram has angle measure of 20, 160, 20, 160. Can you conclude that it is a rhombus, a rectangle, or a square?
no
Suppose the diagonals of a quadrilateral bisect each other. Can you conclude that it is a rhombus, a rectangle, or a square?
no
If a quadrilateral is a rectangle, then it is a parallelogram.
true
If a quadrilateral is a parallelogram, then it is a rhombus
false
If a quadrilateral is a square, then it is a rhombus
true
If a quadrilateral is a rectangle, then it is a rhombus
false
If a rhombus is a square, then it is a rectangle
true
What can contain obtuse angles?
parallelogram, rhombus
What contains no acute angles?
rectangle, square
If a quadrilateral is a kite, then its diagonals are _____
perpendicular
The parallel sides of a trapezoid is called ___
bases
The two angles that share a common base of the trapezoid are called ____
base angles
What are the three trapezoids?
Scalene, right, isosceles
The diagonals of an isosceles trapezoid are ___
congruent
A ____ is a quadrilateral with exactly two pairs of congruent consecutive sides
kite
A kite has exactly one pair of opposite ___ congruent
angles
If a trapezoid has one pair of congruent base angles, then it is ____
parallel
A trapezoid is isosceles if and only if its ___ are congruent
legs
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