Alternate Interior Angles

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• Alternate Interior Angles
• High School Geometry
• Aligned to Common Core State Standards

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Teacher Notes
Insight 360 is eInstructions classroom
instruction system that allows you to interact
with your students as they learn, quickly gaining
insight into student understanding during class
so you can adjust instruction in real-time during
a single class session. Use this content,
designed specifically for use with Insight 360,
to interact with your class. This content
includes brief instructional material and two
types of activities 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.
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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). Angles 4 and 5 are also
alternate interior angles.
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Alternate Exterior Angles
Based on what you know about alternate interior
angles, which angles would be alternate exterior
angles?
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Alternate Exterior Angles
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.
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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?
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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? Angles 3
and 5 are same-side interior angles. Angles 4 and
6 are same-side interior angles.
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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?
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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? Angles 3 and 7,
angles 2 and 6, and angles 4 and 8 are also pairs
of corresponding angles.
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Corresponding Angles Postulate
If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
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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



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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
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Congruent Angles Activity
If m ?? n and a ?? b, find all the angles
congruent to ?6.
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Congruent Angles Activity

• If m ?? n and a ?? b, find all the angles
  congruent to ?6.
• ?2, ?3, ?7, ?10, ?11, ?14, ?15

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• Given m ?? n, find the value of x.

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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

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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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