Download Warm up: Replace the with , or =. 1. AB BC 2. m A m B 3.

Warm up: Replace the with <, >, or =.
B
A
45°
45°
135°
C
OBJECTIVE: You will learn to identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem.
Section 7­2
D
_____________________
D
1. AB BC
3
2. m A m B
exterior angle ­­
1
G
2
F
4
3. m BCA m A
E
remote interior angle ­­
4. AD AC
5. m A m BCD
Example 1: Name the remote interior angles with respect to 1.
1
2
11
12 10
2
3
4 5
Example 2: In the figure, 2 and 3 are remote interior angles with respect to what angle?
4 1
5 6
3
9
7 8
1
Exterior Angle Theorem ­­The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
Example 3: If m 2 = 38 and m 4 = 134, what is m 5?
56
m 1 = m 3 + m 4
1
3 4
2
D
3
1
G
2
Example 4: If m 2 = x + 17, m 3 = 2x, and m 6 = 101, find the value of x.
4
F
E
Exterior Angle Inequality Theorem
­­ The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles.
Theorem 7­5 ­­ If a triangle has one right angle, then the other two angles must be acute.
Example 5: Name two angles in MAL that have measures less than 90.
M
m 1 > m 3 and m 1 > m 4
1
D
3
1
G
F
3
2
C
4
L
2
A
E
2
A
Guided Practice:
1. Draw a triangle and extend all of the sides. Identify an exterior angle at each of the vertices.
X
1 2
B
3
4
5
K
L
2. Name two remote interior angles with respect to AKL.
3. If m 3 = 65 and m 5 = 142, what is m 2?
4. If m 1 = 2x ­ 26, m 3 = x, and m 4 = 37,
find the value of x.
5. Replace with <, >, or = to make a true sentence.
m 3 m 1
Do you have any Vocab questions?
OBJECTIVE:
HOMEWORK: p. 286 ­ 287
# 8 ­ 22
***Quiz next time over section 7­1***
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