Section 7'1 Triangle Application Theorems

1
Section 7.1Triangle Application Theorems
mÐ1 mÐ2 mÐ3 __?___ Choose one (lt, gt, )
mÐ1 mÐ2 _?__mÐ4
2
1
3
4

• (Remember from Chapter 5..)
• Exterior Angle An angle that is adjacent to and
  supplementary to an interior angle of a triangle/
  polygon.
• Theorem The measure of an exterior angle of a
  triangle is equal to the sum of the measures of
  the remote interior angles.

2

• Given Diagram as marked
• Find x, y, and z

55º
100º
z
y
60º
x
55º
3

• The measure of D is twice that of E.
• 1 150º
• Find the measure of each angle of the triangle.

D
1
C
E
4

• Find the measure of the angle formed by the
  bisectors of the other two angles.

A
80º
E
C
B
5
Triangle Sum Theory
6
Triangle Sum Theory
7
Triangle Sum Theory
8
Section 7.1 Triangle Application Theorems
B
Given D is the midpoint of AB E is the midpoint
of BC DE _at_ EF Prove DE AC
E
F
D
V
V
C
A

• Midline Theorem A segment joining the midpoints
  of two sides of a triangle is parallel to the
  third side, and its length is one-half the length
  of the third side

9
Section 7.2 Triangle Theorems

• No Choice Theorem
• If two angles of one triangle are congruent to
  two angles of a second triangle, then the third
  angles are congruent.
• The triangles need not be congruent to apply this
  theorem
• AAS
• If there exists a correspondence between the
  vertices of 2 triangles such that 2 angles and a
  nonincluded side of one are congruent to the
  corresponding parts of the other, then the
  triangles are congruent!
• Similar use to SAS, SSS, and ASA.

10
Proving Triangles Congruent (AAS)

11
Proving Triangles Congruent (AAS)
Section 7.2
12
Proving Triangles Congruent (AAS)
Section 7.2
13
Proving Triangles Congruent (AAS)
Section 7.2
14
Proving Triangles Congruent (AAS)
Section 7.2
15
Proving Triangles Congruent (AAS)
Section 7.2
16
Proving Triangles Congruent (AAS)
Section 7.2
17
Proving Triangles Congruent (AAS)
Section 7.2
18
Proving Triangles Congruent (AAS)
Section 7.2
19
Proving Triangles Congruent (AAS)
Section 7.2
20
Proving Triangles Congruent (AAS)
Section 7.2
21
Proving Triangles Congruent (AAS)
Section 7.2
22
Page 304 6
M
K
O
J
G
H
23
Page 304- 7
Y
Z
A
V
B
X
24
Page 305 - 14
Z
A
C
X
Y
B
25
Section 7.3 Formulas Involving Polygons
The sum of the measures of the interior angles of
a polygon is (n-2)180.

• Naming Polygons
• 3 Triangle
• 4 Quadrilateral
• 5 Pentagon
• 6 Hexagon
• 7 Heptagon
• 8 Octagon
• 9 Nonagon
• 10 Decagon
• 12 Dodecagon
• 15 Pentadecagon
• n n-gon

What is the sum of the measures of the exterior
angles of a polygon?
The number of diagonals that can be drawn in a
polygon is n(n-3)/2
26
Section 7.4 Regular Polygons

• Regular Polygons are polygons that are both
  equilateral and equiangular.