BY : ANA JULIA
ROGOZINSKI
-A polygon is a shape with three or more -Polygons can be classified
sides; a closed figure made by joining
according to the number
line segments .
of sides it has.
Polygons
Not polygons
-Each segment that forms a polygon is a side
of a polygon. The common endpoints of 2 sides
is a vertex. A segment that connects any two
nonconsecutive vertices is a diagonal.
-You can describe a polygon by comparing the
length of its sides or the measure of its angles.
Name of
polygon
Number of sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Undecagon
11
Dodecagon
12
Tell whether the figure is a polygon or not. If it is classify it by the
number of sides it has.
2. NO
1.Yes, and it’s an
octagon
3.Yes, it is a
triangle
-A concave polygon has
one vertex pointing
inward.
-A convex polygon has all
vertices pointing outward.
Tell if each shape is
concave or convex.
1.
Concave
2.
Convex
3.
Concave
All the sides are the same
(congruent).
All the angles are the same
(congruent).
A regular polygon is both of
them.
Tell if each shape is equiangular,
equilateral or a regular polygon?
1.equiangular
2. Regular
3. Equilateral
- This theorem states that any time you add
up 1 side you add 180 to the sum it needs to
sum.
1.
2.
Find the interior
angles of a triangle.
(3-2)180
1 x 180= 180
180 / 3 = 60
Find the interior angles
of a nonagon.
(9-2) 180
7 x 180= 1260
1260 / 9 = 140
3. Find the interior
angles of a pentagon.
(5-2) 180
3 x 180 = 540
540 /3 = 180
Theorem 6-2-1:
Converse:
If a quadrilateral is a
parallelogram, then its
opposite sides are
congruent
B
A
M
C
D
If the opposite sides of a
quadrilateral are congruent,
then it is a parallelogram.
V
L
1. AB is congruent to CD
T
Tell whether it is a
parallelogram or not?
NO
YES
2. MV is congruent to TL
3. BC is congruent to DA
4. ML is congruent to VT
YES
Theorem 6-2-2
If a quadrilateral is a parallelogram, then its
opposite angles are congruent.
Converse:
If the opposite angles in a quadrilateral
are congruent, then it is a parallelogram.
1.<A is congruent to <D
2.<B is congruent to <C
3. To what
angle would <M be
congruent to? <N
Theorem 6-2-3:
If a quadrilateral is a parallelogram,
then its consecutive angles are
supplementary.
Converse:
If the consecutive angles of a
quadrilateral are
supplementary, then it is a
quadrilateral
1.
2.
3.
4.
m<A + m<B = 180
m<C + m<D = 180
m<B + m< D = 180
Would measurement of angle A and
angle D be supplementary ? NO,
because they are not consecutive
angles and they don’t sum 180
Theorem 6-2-4:
If a quadrilateral is a
parallelogram, then it’s
diagonals bisect each other?
Converse:
If the diagonals of a quadrilateral
bisect each other then it is a
parallelogram.
1. AO is congruent to DO
2. CO is congruent to BO
3.What can you tell in this
diagonals?
That DM is congruent to BM
and that AM is congruent to
CM
- A parallelogram is a quadrilateral that has opposite
sides parallel to each other or it has two pair of
parallel lines.
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Diagonals bisect each other
5. A quadrilateral that has a opposite
sides parallel to each other.
6. One set of congruent and parallel sides.
Tell whether you each figure is a parallelogram or
it isn’t.
1.No
3.Yes
2. Yes
-A square is a parallelogram that is both a
rectangle and a rhombus meaning that all
its sides are congruent and all the angles
have the same measurement. (It is a
regular polygon).
1. 4 congruent sides and angles
2. Diagonals are congruent and perpendicular.
1. How can you tell by the diagonals that the
figure is a square?
--You can tell it is a square by the diagonals
being perpendicular and congruent.
Tell whether it is a square
NO
YES
A rhombus is a parallelogram with 4 congruent
sides.
-
1. Diagonals are perpendicular
-6-4-3: If a quadrilateral is a rhombus, then it is a parallelogram.
-6-4-4: If a parallelogram is a rhombus, then its diagonals are perpendicular
-6-4-5: If a parallelogram is a rhombus, then each diagonal bisects a pair of
opposite angles.
Tell whether it is a
rhombus?
YES
YES
NO
- A rectangle is a parallelogram with 4 right
angles.
1. Diagonals are congruent
-6-4-2:If a quadrilateral is a rectangle ,
then it is a parallelogram.
-6-4-2: If a parallelogram is a rectangle,
then its diagonals are congruent.
1. What can you say about the
diagonals of this triangle? That
AC is congruent to BD
If side MN = 12 and side ML
= 5, what is the length of
the other two sides?
2.LO = 12
3. NO= 5
-A square is both a rectangle and a rhombus
together including all its properties. A rectangle
has 4 congruent angles and diagonals are
congruent while a rhombus has all 4 congruent
sides and diagonals are perpendicular.
- A trapezoid is a quadrilateral with one pair of
parallel sides.
- Is a trapezoid with a pair of
congruent legs.
1. Diagonals are congruent
2. Base <‘s are congruent
3. Opposite ,’s are supplementary
-6-6-3: If a quadrilateral is an isosceles
trapezoid then each pair of base angles
are congruent.
-6-6-4:If a trapezoid has one pair of
congruent base angles then the trapezoid
is isosceles.
-6-6-5:A trapezoid is isosceles if and only
if its diagonals are congruent.
E
F
2. YB is parallel to EF
3. YB is parallel to MT
Y
M
B
T
- A kite has two pairs of adjacent sides.
1. Diagonals are congruent
2. One pair of congruent angles (the ones
formed by non-congruent sides)
3. One of the diagonals bisects the other.
-6-6-2: If a quadrilateral is a kite, then its diagonals are perpendicular.
-6-6-2: If a quadrilateral is a kite, then exactly one pair of opposite angles are
congruent.
1. < R is congruent to <P
3. The diagonals of the kite
are intersecting at right
angles.
2. It has two pairs of
congruent consecutive
sides.