Alternate Interior Angles
High School Geometry
Aligned to Common Core State Standards
Teacher Notes
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Constructed Response Activity for students to complete as an individual
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Assessment Item with CueTag™ for students to respond to via student
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Definition of Alternate Interior Angles
Two angles that lie between two lines and on the opposite sides of a third line
are called alternate interior angles.
In the drawing below, 3 and 6 would be alternate interior angles since
they are inside the blue parallel lines and on opposite (alternate) sides of the
transversal (red line).
2
1
3
4
5
6
7
8
Angles 4 and 5 are also alternate interior angles.
Alternate Exterior Angles
Based on what you know about alternate interior angles, which angles would
be alternate exterior angles?
2
1
3
4
5
6
7
8
Alternate Exterior Angles
Based on what you know about alternate interior angles, which angles would
be alternate exterior angles?
2
1
3
4
5
6
7
8
Angles 1 and 8 are alternate exterior angles.
Angles 2 and 7 are alternate exterior angles.
Same-side or Consecutive Interior Angles
Based on what you know about alternate interior angles, which angles would
be same-side or consecutive interior angles?
2
1
3
4
5
6
7
8
Same-side or Consecutive Interior Angles
Based on what you know about alternate interior angles, which angles would
be same-side or consecutive interior angles?
2
1
3
4
5
6
7
8
Angles 3 and 5 are same-side interior angles.
Angles 4 and 6 are same-side interior angles.
Corresponding Angles
Corresponding angles lie on corresponding sides of the two lines and on the
same side of the third line. Angles 1 and 5 are corresponding angles. What
other pairs of angles are corresponding angles?
2
1
3
4
5
6
7
8
Corresponding Angles
Corresponding angles lie on corresponding sides of the two lines and on the
same side of the third line. Angles 1 and 5 are corresponding angles. What
other pairs of angles are corresponding angles?
2
1
3
4
5
6
7
8
Angles 3 and 7, angles 2 and 6, and angles 4 and 8 are also pairs of
corresponding angles.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then corresponding angles are
congruent.
2
1
3
4
5
6
7
8
Prove alternate interior angles are congruent.
If two lines are parallel, prove alternate interior angles are congruent.
Given: m  n
Prove: 4  5
m  n
Given
m
n
1 2
3 4
5 6
7 8
Prove alternate interior angles are congruent.
If two lines are parallel, prove alternate interior angles are congruent.
Given: m  n
Prove: 4  5
Answers may vary.
m  n
Given
1  5
Corresponding angles are congruent.
1  4
Vertical angles are congruent.
4  5
Substitution
m
n
1 2
3 4
5 6
7 8
Congruent Angles Activity
If m  n and a  b, find all the angles congruent to 6.
a
b
1 2
3 4
9 10
11 12
5 6
7 8
13 14
15 16
m
n
Congruent Angles Activity
If m  n and a  b, find all the angles congruent to 6.
2, 3, 7, 10, 11, 14, 15
a
b
1 2
3 4
9 10
11 12
5 6
7 8
13 14
15 16
m
n
Given m  n, find the value of x.
m
68
n
104
(5x+4)
Create Your Own
Create your own problem to find a missing angle measure using parallel lines
and alternate interior angles. Your problem must include the following:
• a diagram
• given information
• 3 or more steps to solve
Create Your Own
Create your own problem to find a missing angle measure using parallel lines
and alternate interior angles. Your problem must include the following:
• a diagram
• given information
• 3 or more steps to solve
Answers will vary.
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