Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Group action wikipedia , lookup

Simplex wikipedia , lookup

Multilateration wikipedia , lookup

Riemann–Roch theorem wikipedia , lookup

Complex polytope wikipedia , lookup

Four color theorem wikipedia , lookup

Noether's theorem wikipedia , lookup

Euler angles wikipedia , lookup

Integer triangle wikipedia , lookup

Trigonometric functions wikipedia , lookup

Brouwer fixed-point theorem wikipedia , lookup

History of trigonometry wikipedia , lookup

Rational trigonometry wikipedia , lookup

Euclidean geometry wikipedia , lookup

Pythagorean theorem wikipedia , lookup

Transcript
```7.1 Notes
Tuesday, December 02, 2008
1:45 PM
Theorem 50: The sum of the measures of the three angles of a
triangle is 180
Proof:
Given: ABC
Prove: mBAC + m B + mC = 180
A
m
C
B
Definition: An Exterior angle of a polygon is an angle that is
adjacent to and supplementary to an interior angle of the
polygon.
Notes Page 1
ext 
Theorem 51: The measure of an exterior angle of a triangle is
equal to the sum of the measure of the remote interior angles.
M 1 = mA + mC
A
1
C
B
Midline Theorem: A segment joining the midpoint of two sides
of a triangle is parallel to the third side, and its length is onehalf the length of the third side.
A
D
E
C
B
Example 1:
80
Notes Page 2
80
100 
z
55
60
y
x
Example 2:
Find the mD
A
80
D
x
x
y
y
B
C
Notes Page 3
7.2 Notes
Wednesday, December 03, 2008
10:45 AM
No Choice Theorem:
If two angles of one triangle are congruent to two angles of a
second triangle, then the third angles are congruent.
C
F
A
B
D
AAS Theorem: We already use it :)
Example 1:
Given: A  D
Prove: E  C
D
A
B
C
E
Statements
1. A  D
Reasons
1. Given
Notes Page 4
E
2. ABE  DBC 2. Verticals 's are 
3. E  C
3. No choice theorem
Notes Page 5
7.3 notes
Thursday, December 04, 2008
7:51 AM
# of sides
3
4
5
6
7
8
9
10
12
15
n
Polygon
Triangle
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
Theorem 55: The sum Si of the measures of the angles of a
polygon with n sides is given by the formula S i = (n - 2)180.
B
B
C
B
C
A
A
A
C
D
D
E
Si= 180
Si= 360
Notes Page 6
Si= 540
Theorem 56: If one of the exterior angles is taken at each
vertex, the sum SE of the measures of the exterior angles of
a polygon is given by the formula S E = 360.
2
3
1
4
5
m1 + m2 + m3 + m4 + m5 = 360
Theorem 57: The number of diagonals that can be
drawn in a polygon of n sides is given by the formula
n(n  3)
d
2
Example 1: Find the sum of the measures of the
angles in a hexagon.
Example 2: Find the number of diagonals that can be
drawn in a heptagon.
Notes Page 7
Example 3:
What is the name of a polygon if the sum of the
measures of its interior angles is 1080?
Notes Page 8
7.4 Notes
Thursday, December 04, 2008
12:58 PM
Definition: A regular polygon is a polygon that is both
equilateral and equiangular.
equilateral triangle
square
Regular
Pentagon
Theorem 58: The measure of E of each exterior angle of an
equiangular polygon of n sides is given by the formula
E
360
n
Example 1:
How many degrees are there in each exterior angle of a regular
pentagon?
Example 2:
How many degrees are there in each interior angle of a regular
pentagon?
Notes Page 9
pentagon?
Example 3:
If each exterior angle of a polygon is 18, how many sides does
the polygon have?
Notes Page 10
```
Related documents