Download polygons salvador amaya

Salvador Amaya 9-5
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A polygon is a closed figure that has no
curved sides. Therefore, it needs to have at
least three sides.
Not a
polygon
Yes, a
polygon
Yes, a
polygon
Exterior Angle
Interior angle
Diagonal
Side
Vertex
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Interior angle: angle in the inside of a polygon
Exterior angle: angle in the outside of a
polygon
Vertex: point where two lines meet
Diagonal: segment that connects two
vertices of a polygon
Side: segment in a polygon
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Concave polygon: polygon that has a vertex
that points in
Convex polygon: polygon that has all vertices
pointing out.
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Concave
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Convex
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Equilateral: All sides measure the same.
Equiangular: All the angles measure the
same.
Equilateral and Equiangular = Regular
Polygon
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Equilateral
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Equiangular
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Regular
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The sum of the interior angles of a polygon is
(n-2) x 180, being n the number of sides in the
polygon.
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What is the sum of interior angles for a
nonagon?
(n-2) x 180
(9-2) x 180
7 x 180
1260
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What is the measure of an angle in a regular
hexagon?
[(n-2) x 180] / n
[(6-2) x 180] / 6
(4x 180) / 6
720 / 6
120
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What is the sum of the interior angles for a
pentagon?
(n-2) x 180
(5-2) x 180
3 x 180
540
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If a quadrilateral is a parallelogram, then
opposite sides are congruent.
If BACD, KHIJ, and FEGH are parallelograms, then….
a
c
e
d
b
AC is cong. To
BD, AB is cong.
to CD, EF is
cong. to GM,
EG is cong. to
FM, HI is cong.
to KJ, HK is
cong. to IJ.
g
h
i
f
k
j
m
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If opposite sides in a quadrilateral are
congruent, then the quadrilateral is a
parallelogram.
If AC is cong. To BD, AB is cong. to CD, EF is cong. to GM, EG is cong. to FM, HI is cong. to KJ,
HK is cong. to IJ, then….
a
c
68
e
13
13
68
d
b
27
22
g
h
4
k
8
i
f
22
27
8
4
j
BACD, KHIJ, and
FEGH are
parallelograms
m
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If a quadrilateral is a parallelogram, then
opposite angles are congruent.
If BACD, KHIJ, and FEGH are parallelograms, then….
a
c
e
<a is cong. to <d, <c is cong.
to <b, <e is cong. to <m, <f is
cong. to < g, <h is cong. to
<j, <k is cong. to <i
d
b
g
h
i
f
k
j
m
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If opposite angles are congruent in a
quadrilateral, then the quadrilateral is a
parallelogram.
If <a is cong. to <d, <c is cong. to <b, <e is cong. to <m, <f is cong. to < g, <h is cong. to <j, <k
is cong. to <i, then….
a
128
52
c
e
36
52
128
d
b
144
h
97
k
83
83
97
j
i
f
144
BACD, KHIJ, and FEGH are
parallelograms
36
m
g
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If a quadrilateral is a parallelogram, then the
consecutive angles add up to 180.
If BACD is a parallelogram, then….
a
c
<a+<b=180
<b+<d=180
<d+<c=180
<a+<c=180
b
d
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If the consecutive angles in a quadrilateral
add up to 180, then the quadrilateral is a
parallelogram
If <a+<b=180, <a+<c=180, <b+<c=180, <d+<c=180, <e+<g=180, <e+<f=180, <g+<m=180,
<m+<f=180, <h+<i=180, <h+<k=180, <k+<j=180, <j+<i=180, then….
a
135
65
c
e
24
65
135
d
b
156
h
103
k
77
77
103
j
i
f
156
BACD, KHIJ, and FEGH are
parallelograms
24
m
g
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If a quadrilateral is a parallelogram, then the
diagonals bisect each other.
If CABD, and GEFH are parallelograms, then….
a
AL=LD
BL=LC
EK=KH
FK=KG
b
45
f
e
48
29
l
32
k
48
45
32
g
c
d
29
h
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Both pairs of opposite sides are congruent.
Both pairs of opposite angles are congruent.
Its consecutive angles are supplementary.
Its diagonals bisect each other.
It has a pair of congruent parallel sides.
Both pairs of opposite sides are parallel.
All are parallelograms because both their opposite sides are congruent.
6
2
2
6
147
96
33
94
94
33
96
All are parallelograms because both their opposite angles are congruent.
147
All are parallelograms because their consecutive angles add up to 180.
132
48
48
132
91
99
91
99
34
146
146
34
7
5
7
5
All are quadrilaterals because their
diagonals bisect each other.
All are parallelograms
because they have a pair
of congruent parallel
sides.
45
45
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Rhombus: parallelogram with 4 congruent
sides. Its diagonals are perpendicular to each
other.
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If a quadrilateral is a rhombus, then it is a
parallelogram.
Since these are rhombuses because they
are equilateral sides, then they are also
parallelograms.
28
28
28
28
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If a parallelogram is a rhombus, then its
diagonals are perpendicular to each other.
Since these are rhombuses, then their diagonals are
perpendicular to each other
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If a parallelogram is a rhombus, then their
diagonals bisect the opposite angles.
a
Since this is a rhombus, then…
<BAE is cong. to <CAE
<EBA is cong. to <EBD
<BDE is cong. to <CDE
<DCE is cong. to <ACE
e
b
c
d
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If a pair of consecutive sides is congruent,
then the quadrilateral is a rhombus.
Since these are parallelograms,
because they have congruent
consecutive sides, then they are
rhombuses.
98
98
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If the diagonals in a parallelogram are
perpendicular, then it is a rhombus.
Since the diagonals
are perpendicular,
then they are
rhombuses
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If a diagonal bisects a pair of opposite angles,
then it is a rhombus.
Since….
<ZXB is cong. to <CXB, then CXZV is a rhombus
<XZB is cong. to <VZB, then CXZV is a rhombus
<ZVB is cong. to <CVB, then CXZV is a rhombus
<XCB is cong. to <VCB, then CXZV is a rhombus
z
x
b
v
c
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Rectangle: parallelogram with 4 right angles .
Its diagonals are congruent.
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If it is a rectangle, then it is a parallelogram.
Since these are rectangles (4 rt. angles), then they are also
parallelograms.
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If it is a rectangle, then the diagonals are
congruent.
a
c
z
b
w
q
d
AD is cong. to CB
x
ZV is cong. to CX
e
c
v
Since these
are rectangles,
the diagonals
are congruent.
QR is cong. to EW
r
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If a quadrilateral has a right angle, then it is a
rectangle.
They are all rectangles
because they each have a
right angle.
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If the diagonals in a parallelogram are
congruent, then it is a rectangle.
p
o
f
Since
diagonals
are
congruent,
these are
rectangles
i
PU= 15
IO= 15
h
FS=1
GH=1
u
IH=98
JK=98
g
s
l
k
j
h
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Square: parallelogram with 4 sides that are
congruent and angles are congruent. The
diagonals are congruent and perpendicular.
It is both a rhombus and a rectangle.
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2 pairs of congruent consecutive sides.
Perpendicular diagonals.
1 pair of congruent angles.
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If it is a kite, then diagonals are perpendicular.
Since the diagonals in the quadrilaterals are perpendicular, they are
kites.
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If it is a kite, then there is 1 pair of opposite
congruent angles.
103
103
110
110
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One pair of parallel sides.
Base- nonparallel side
Leg- parallel side.
Base angles- angles whose common side is a
base.
Isosceles trapezoid- has 2 congruent legs
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If it is an isosceles trapezoid, then the 2 pairs
of base angles are congruent.
Since these are isosceles triangles,
their base angles are congruent.
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If there are 2 pairs of congruent angles, base
angles, it is an isosceles triangle.
70
110
110
70
Since the base angles
are congruent, these are
isosceles trapezoids.
83
83
97
97
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An isosceles trapezoid has to have congruent
diagonals.
a
g
b
AD is cong. to BC
f
v
b
j
n
c
d
m
VM is congruent to NB
h
These are isosceles trapezoids because their diagonals are congruent.
FJ is cong. to GH
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The midsegment in a trapezoid is parallel to
both bases and it is half as long as the sum of
the two other bases.
(b1+b2)/2
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What is the midsegment of this trapezoid?
(b1+b2)/2
10
10+35/2
45/2
22.5
35
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What is the measure of the missing base?
67-21= 46
46+67= 113
21
67
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What is the midsegment of this trapezoid?
(b1+b2)/2
135
135+11/2
146/2
73
11
_____(0-10 pts.) Describe what a polygon is. Include a discussion about the parts of a polygon. Also
compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular.
Give 3 examples of each.
_____(0-10 pts.) Explain the Interior angles theorem for polygons. Give at least 3 examples.
_____(0-10 pts.) Describe the 4 theorems of parallelograms and their converse and explain how they are
used. Give at least 3 examples of each.
_____(0-10 pts.) Describe how to prove that a quadrilateral is a parallelogram. Give at least 3 examples of
each.
_____(0-10 pts.) Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus,
square and rectangle theorems. Give at least 3 examples of each.
_____(0-10 pts.) Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each.
_____(0-10 pts.) Describe a kite. Explain the kite theorems. Give at least 3 examples of each.