Alternate Interior AnglesHigh School GeometryAligned to Common Core State Standards

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Constructed Response Activity for students to complete as an individual or a group assignment. Send each Constructed Response Activity to the Insight 360 iPad Student App.Assessment Item with CueTag™ for students to respond to via student response devices. Receive instant real-time feedback and longitudinal reports.

Teacher Notes

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).

Angles 4 and 5 are also alternate interior angles.

Definition of Alternate Interior Angles

1 23 4

5 6

7 8

Based on what you know about alternate interior angles, which angles would be alternate exterior angles?

Alternate Exterior Angles

1 23 4

5 6

7 8

Based on what you know about alternate interior angles, which angles would be alternate exterior angles?

Angles 1 and 8 are alternate exterior angles. Angles 2 and 7 are alternate exterior angles.

Alternate Exterior Angles

1 23 4

5 6

7 8

Based on what you know about alternate interior angles, which angles would be same-side or consecutive interior angles?

Same-side or Consecutive Interior Angles

1 23 4

5 6

7 8

Based on what you know about alternate interior angles, which angles would be same-side or consecutive interior angles?

Angles 3 and 5 are same-side interior angles.Angles 4 and 6 are same-side interior angles.

Same-side or Consecutive Interior Angles

1 23 4

5 6

7 8

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?

Corresponding Angles

1 23 4

5 6

7 8

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?

Angles 3 and 7, angles 2 and 6, and angles 4 and 8 are also pairs of corresponding angles.

Corresponding Angles

1 23 4

5 6

7 8

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Corresponding Angles Postulate

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5 6

7 8

If two lines are parallel, prove alternate interior angles are congruent.

Given: m nProve: 4 5

Prove alternate interior angles are congruent.

1 23 4

5 6

7 8n

m

m n Given

If two lines are parallel, prove alternate interior angles are congruent.

Given: m nProve: 4 5Answers may vary.

Prove alternate interior angles are congruent.

m n Given1 5 Corresponding angles are congruent.1 4 Vertical angles are congruent.4 5 Substitution

1 23 4

5 6

7 8

m

n

If m n and a b, find all the angles congruent to 6.

Congruent Angles Activity

1 23 4

5 67 8

9 1011 12

13 1415 16

m

n

a b

If m n and a b, find all the angles congruent to 6.

2, 3, 7, 10, 11, 14, 15

Congruent Angles Activity

1 23 4

5 67 8

9 1011 12

13 1415 16

m

n

a b

Given m n, find the value of x.

104

(5x+4)

68

m

n

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 solveAnswers will vary.

Create Your Own

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