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What about those TRIANGLES?
Triangle Application Theorems
What about those ANGELS?
CB
A1 2
3
ANGLES?Let’s check them out.... I think I’ll draw a line parallel to BC through A....
What about those
CB
A1
23
ANGLES?
What do you know now?
The Sum of the measures of the three angles of a triangle is 180 degrees!
Finally!
Theorem 50
What do we know about exterior angles of a triangle?
Which angles are exterior angles of this triangle?
How many are there? What are their remote interior angles?
C
B
A
211
4
66 5
33
998
77
Exterior angle of a Polygon?
An exterior angle of a polygon is the angle that is adjacent to and supplementary to an interior angle of the polygon.
Y
X
S
NO
G
A
C
ED
2
T
N
E P
A
1
What do we know about exterior angles of a triangle?
What do we already know about the measure of each exterior angle?
C
B
A98 7 6 5
4
32
1
Back to Triangles....
What can we find out about exterior angles of a triangle?
C
B
A
1
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Theorem 51
Here comes a MIDLINE!
ACABM M
CB
A
Midline
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
E D
C
B
A
F
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!
Here’s the middle line....
Hang on...it’s a two parter!
Find x, y, and z
55 x yz
60
10080
Find the measure of the angle formed by the bisectors of the other two angles. (angle BEC)
E
CB
A
yy
xx
80
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
D
PC
T
B
A
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?
A, B, F, and D are midpoints of their respective sides.
R E
D
CF
T
B
A
