Download Geometry G - HCHS Math

Geometry G
Section 7.2
Notes
Target 7.2:
Exterior Angle Theorem
A
The angles of ABC are 2, 3, and 4. We call these
angles the interior angles of the triangle.
2
1 is an exterior angle of ABC.
1
C
An exterior angle of a triangle is an angle that
forms a linear pair with one of the angles of the triangle.
4
3
B
Let’s see how interior and exterior angles of a triangle are related to each other.
Use your protractor to measure each angle and record the measures in the chart.
I.
G
II.
A
1
4 3
C
1
2
4
B
III.
D
3
K
2
4
3
F
1
m1
2
E
I
II
III
What pattern do you see in the measures you found?
m2
m3
m4
H
Remote interior angles of a triangle are the two angles that do not form a linear pair with
the exterior angle. The word remote means distant, or far away.
The measure of an exterior angle of a triangle is equal
to the sum of the measures of its two remote interior angles.
R
2
Remote interior angles
for 1
Exterior Angle
3
1
T
4
S
Adjacent interior
angle for 1
Example: 1 is an exterior angle of RST.
2 and 3 are remote interior angles with respect to 1.
In the chart below, list the:
exterior angles and their
remote interior angles.
4
5
2
1
3
Exterior Angle
Remote Interior Angles
6
Warning: Important Information Ahead…
The measure of an exterior angle of a triangle is equal
to the sum of the measures of its remote interior angles.
The measure of an exterior angle of a triangle is greater
than the measure of either of its remote interior angles.
Use the figure at the right to fill in the blanks.
B
1
1. _______ is an exterior angle of KYJ.
2
2. _______ and ________ are remote interior
angles with respect to exterior 8 in KNJ.
K
3. 8 is an exterior angle of ________.
6
Y
Replace each blank with < or > to make a true sentence.
6. m7 ___ m2
7. m8 ___ m4
8. m3 ___ m8
3 9
7
5
4. 1 and 4 are remote interior angles with
respect to exterior 9 in _________.
5. m1 ___ m7
8
N
4
J
10. Use the diagram at the right to:
N
120
x
H
a. Solve for x
(3x - 4)
A
b. Find mA
11. Use the diagram at the right to:
A
a. Solve for x
B
b. Find mACD
24
(2x – 18)
C
D