Download Slide 1 - Mrs. Hille`s FunZone

curve—continuous set of
points (includes lines)
simple curves—do not
intersect themselves
closed curves—start and end
at same point
simple
closed
simple
closed
simple,
not closed
closed,
not simple
Polygon
A polygon is a simple closed
plane figure made up of line
segments.
Convex Polygon
A convex polygon is a
polygon in which all interior
angles have measures less
than 180°.
Concave Polygon
A concave polygon is a
polygon in which at least one
interior angle has a measure
greater than 180°.
Types of Polygons
convex
concave
side—segment making up
part of a polygon
vertex—corner of a polygon;
where two sides meet
Number of Sides
Name
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
Number of Sides
Name
8
octagon
9
nonagon
10
decagon
12
dodecagon
n
n-gon
regular polygon—all sides
same length, all angles same
measure
Example 1
Name each polygon and
indicate whether it is regular.
D
C
A
B
ABCD is a quadrilateral.
Example 1
Name each polygon and
indicate whether it is regular.
I
H
G
J
E
F
EFGHIJ is a regular hexagon.
scalene triangle: A triangle
with no two sides equal in
length.
isosceles triangle: A triangle
with at least two sides equal
in length.
equilateral triangle: A triangle
with all sides equal in length.
60°
45°
75°
acute triangle: three acute
angles
50°
40°
right triangle: one right angle
20°
30°
130°
obtuse triangle: one obtuse
angle
Example 2
Classify each triangle
according to the measures of
its angles and the lengths of
its sides.
B
A
C
ABC is obtuse scalene.
E
D
F
DEF is right isosceles.
H
G
I
GHI is acute equilateral.
Theorem
In any triangle, the sum of
the measures of the angles
is 180°: in ABC m A +
m B + m C = 180°.
Example 3
Write and solve an equation
to find m X.
X
?
Y
116°
22°
Z
Example 3
m X + m Y + m Z = 180
m X + 116 + 22 = 180
m X + 138 = 180
m X = 42°
Quadrilateral
A quadrilateral is a
four-sided polygon.
Trapezoid
A trapezoid is a quadrilateral
with at least one pair of
parallel sides.
Parallelogram
A parallelogram is a
quadrilateral with two pairs
of parallel sides.
Rectangle
A rectangle is a
parallelogram with four right
angles.
Rhombus
A rhombus is a
parallelogram with four
congruent sides.
Square
A square is a rectangle with
four congruent sides.
Diagonal
A diagonal is a line segment
joining any two nonadjacent
vertices of a polygon.
Triangle
number of
diagonals from
one vertex
number of
sides, n
number of
triangles formed
sum of angle
measures
3
1
180°
Quadrilateral
number of
diagonals from
one vertex
number of
sides, n
number of
triangles formed
sum of angle
measures
4
2
2(180) = 360°
Pentagon
number of
diagonals from
one vertex
number of
sides, n
number of
triangles formed
sum of angle
measures
5
3
3(180) = 540°
Hexagon
number of
diagonals from
one vertex
number of
sides, n
number of
triangles formed
sum of angle
measures
6
4
4(180) = 720°
Example 4
Find the sum of the
measures of the angles in a
regular octagon.
6(180) = 1,080°
Example 4
Find the measure of each
angle in a regular octagon.
1,080 = 135°
8
Example 5
Write and solve an equation
to find m A.
C
B
80°
55°
120°
A
D
Example 5
m A + 80 + 55 + 120 = 360
m A + 255 = 360
m A + 255 – 255 = 360 – 255
m A = 105°