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Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
B
A
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
B
A
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
B
A
C
The parallel postulate allows us to draw a
line through point B that is parallel to AC.
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
3
A
B
2 1
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
3
A
B
2 1
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
3
A
B
2 1
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
3
A
B
2 1
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.
Theorem 51: The measure of an exterior
angle of a triangle is equal to the sum of the
measures of the remote interior angles.
B
A
1
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.
B
A
1
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.
B
A
1
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.
B
A
1
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.
B
A
1
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.
B
A
1
C
Theorem 52: 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.
(Midline Theorem)
Theorem 52: 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. (Midline Theorem)
B
A
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
•
C
Points D and E are midpoints.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
•
C
Points D and E are midpoints.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
•
C
Points D and E are midpoints.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Extend DE so that E is the midpoint of DF.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
We can draw CF, because two points determine
a line.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Triangle BED is congruent to triangle CEF by
SAS.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
ADFC is a parallelogram, because one pair of
opposite sides is both parallel and congruent.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
DF
E
F
•
C
to AC, because opposite sides of a
parallelogram are parallel.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
DE to AC, because DE is part of DF.
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 52: 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. (Midline Theorem)
B
D
•
A
E
F
•
C
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
Theorem 51: The measure of an exterior
angle of a triangle is equal to the sum of the
measures of the remote interior angles.
Theorem 50: The sum of the measures of the
three angles of a triangle is 180º.
(Triangle Sum Theorem)
Theorem 51: The measure of an exterior
angle of a triangle is equal to the sum of the
measures of the remote interior angles.
Theorem 52: 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.
(Midline Theorem)