Download 7.1 –3 Triangle Application Theorems

Geo
7.1 & 7.2 Notes
Sum of the
7.1 –3 Triangle Application
Theorems
angles of a triangle (1):
Theorem: The sum of the measures of the three angles in a triangle is _________.
Proof:
1
B
2
3
C
A
Example #1
Find: x, y, and z
80
100
z
55
y
x
Example #2
Find the measure of the angle formed by the bisectors.
y
y
60
80
x
x
Exterior Angle Theorem (2):
Theorem: The measure of an exterior angle of a triangle is equal to the sum of the
measures of the ______________________________________.
Proof:
A
1
B
C
Given: m1 = 150 and mD is twice that of E.
Find: The measure of each angle in the triangle.
Example #3
D
E
1
F
Midline Theorem (3) :
Theorem: A segment joining the midpoints of two sides of a triangle is parallel to
the third side and its length is ½ the length of the third side.
A
Given:
P is the midpoint of AB
S is the midpoint of AC
BC = 12cm
mAPS = 70
Then: PS = ________
mABC = ________
P
B
S
C