Transcript What about those TRIANGLES?

What about those
TRIANGLES?
Triangle Application Theorems
What about those ANGELS?
ANGLES?
Let’s check them out.... I think I’ll draw a line parallel to BC
through A....
A
1
B
2
3
C
What about those ANGLES?
A
1
2
B
What do you know now?
3
C
Theorem 50
The Sum of the measures of
the three angles of a triangle
is 180 degrees! Finally!
What do we know about
exterior angles of a triangle?

Which angles are exterior angles of this triangle?
1
2
B
9
8


A
7
3
4
C
6
5
How many are there?
What are their remote interior angles?
Exterior angle of a Polygon?
O
T
N
G
S
A
N
A
X
E

1
P
C
Y
E
D
2
An exterior angle of a polygon is the
angle that is adjacent to and
supplementary to an interior angle of
the polygon.
Back to Triangles....
What do we know about exterior
angles of a triangle?

What do we already know about the
measure of each exterior angle?
2
1
3
B
9 A
8 7
C 4
6 5
What can we find out about
exterior angles of a triangle?
1
A
B
C
Theorem 51
The measure of an exterior
angle of a triangle is equal to
the sum of the measures of
the remote interior angles.
Here comes a MIDLINE!
B
C
M AB
Midline
M AC
A
A Midline is a segment that joins the
midpoint of two sides of a triangle.
What’s so special about a
MIDLINE?
Let’s investigate...
Extend ED through D to a point F
so that ED = DF
B
E
A
D
F
C
Here’s the middle line....
Midline Theorem
Hang on...
it’s a two parter!
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!
Find x, y, and z
80
100
z
55
x
y
60
Find the measure of the angle formed by
the bisectors of the other two angles.
(angle BEC)
A
80
E
B
x
x
y
y
C
TRAP is an isosceles trapezoid. What is the
most descriptive name for the figure formed by
connecting the midpoints of the sides of TRAP?
R
E
A
B
D
P
T
C
B, C, D and E are midpoints of their respective sides.
RECT is an rectangle. What is the most
descriptive name for the figure formed by
connecting the midpoints of the sides of RECT?
R
A
E
D
B
T
C
F
A, B, F, and D are midpoints of their respective sides.