Transcript Document

TRIANGLE-SUM THEOREM
During this lesson, you will:
Find the sum of the angles of a
triangle
Use exterior angles of triangles
Classify each triangle based upon
its angle measures:
ACUTE
OBTUSE
RIGHT
EQUIANGULAR
INVESTIGATION
3
INVESTIGATIVE RESULTS:
THEOREM
Triangle Sum Conjecture:
The sum of the measures of the
interior angles of any triangle is 180º
▲ Sum = 180.
B
A
mA + m  B + m  C = 180
C
Ex. 1
Z
Find m Z
X
48º
mX + mY + mZ = 180
48 + 67 + mZ = 180
115 + mZ = 180
mZ = 65
67º
Y
Ex. 2
Find the values
of a, b and c.
C
EX. 2
cº 70º
Find c
aº
c + 70 = 90
A
c = 20º
D
Find a. Use Triangle Sum
a + mADC + c = 180
a + 90 + 20 = 180
a + 110 = 180
a = 70º
bº
B
Find b.
Use
Triangle Sum
b = 20º
Use your triangle sum conjecture to calculate
the measure of the third angle in each triangle
below.
Third Angle Conjecture:
If two angles of one triangle are equal in
measure to two angles of another triangle, then
the remaining angles _____________________.
7
Exterior Angle Theorem
Remote interior
angles
A
B
2
Exterior angle
1
3
x
C
m x = m  1 + m  2
The measure of an
exterior angle in any
triangle equals the
sum of the two
remote interior angles.
1. Measure the angles of your triangle that you traced.
2. Extend one side of your triangle:
3. Measure that exterior angle
Geometry
Mrs. McConaughy
9
Examples:Justify your answer. x = ____
x
x + y = _____
30
x
y
135
x = ____
x
x
x
90
45
144
x = ____