This document discusses linear angles formed by parallel lines intersected by a transversal. It provides definitions and theorems about corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles, and same-side exterior angles. Students will use deductive reasoning and these definitions and theorems to proficiently justify properties of linear angles in geometric proofs. The document outlines tools and examples students can use in their practice and assessment of these skills.

1. LINEAR ANGLES
August 15th
Assessment day!
August 16th
Learning outcome:
How do we use deductive reasoning to
proficiently justify geometric properties?

2. WARM – UP LINEAR ANGLES FORMED BY
PARALLEL LINES
1.If two parallel lines are
intersected by a
transversal, what relations
exist among the measures of
the angles formed?
a. If < 1 = 110° Find the
measures of all the other
angles.

3. LABELLING ANGLES

4. TOOLKIT
Justifcation
Statement
Definition OR
If-Then
Statement
Picture Relationship
(Congruent OR
Supplementar
y)
Check when
ready to be
used in a proof
Definition of
Linear Pair
Definition of
Vertical Angles
Linear Pair
Postulate
Vertical Angle
Theorem

5. TOOLKIT
Justifcation
Statement
Definition OR
If-Then
Statement
Picture Relationship
(Congruent OR
Supplementar
y)
Check when
ready to be
used in a proof
Definition of
Corresponding
Angles
Definition of
Alternate
Interior Angles
Definition of
Alternate
Exterior Angles
Definition of
Same-Side
Interior Angles
Definition of
Same-Side

6. TOOLKIT
Justification
Statement
Definition OR
If-Then
Statement
Picture Relationship
(Congruent OR
Supplementar
y)
Check when
ready to be
used in a proof
Corresponding
Angle
Assumption
Alternate
Interior Angle
Postulate
Alternate
Exterior Angle
Postulate
Same-Side
Interior Angle
Postulate
Same-Side
Exterior Angle

7. EXPLORE - PAGE 36 #4
Given
Linear Pair Postulate
Corresponding Angles
Substitution
Definition of Supplementary
If two parallel lines are cut by a transversal, then
__________________ angles are _____________________.
Vertical Angle Theorem

8. TOOLKIT
Justifcation
Statement
Definition OR
If-Then
Statement
Picture Relationship
(Congruent OR
Supplementar
y)
Check when
ready to be
used in a proof
Corresponding
Angle
Assumption
Alternate
Interior Angle
Postulate
Alternate
Exterior Angle
Postulate
Same-Side
Interior Angle
Postulate
Same-Side
Exterior Angle

9. EXPLORE - PAGE 37 #5
 If two parallel lines are cut by a transversal, then same-side
exterior angles are ________________.
 If two parallel lines are cut by a transversal, then alternate
interior angles are _________________.
 If two parallel lines are cut by a transversal, then alternate
exterior angles are _________________.
Given
Linear Pair Postulate Corresponding Angles Assumption
Substitution
Definition of Supplementary
Vertical Angle Theorem

10. SUMMARY - GALLERY WALK
 Were the requirements of a proficient proof met?
 Does the argument have any errors?
 Does it show the statement is true for all numbers or for some
numbers?
 Does the argument show why the statement is true?
 Does the argument provide an easy way to convince a skeptic?
 Return to your proof and read your feedback.
 Write a final draft of your proof.

11. TOOLKIT
Justifcation
Statement
Definition OR
If-Then
Statement
Picture Relationship
(Congruent OR
Supplementar
y)
Check when
ready to be
used in a proof
Corresponding
Angles
Postulate
Alternate
Interior Angles
Postulate
Alternate
Exterior Angles
Postulate
Same-Side
Interior Angles
Postulate
Same-Side
Exterior

12. CLASSWORK – P. 32-33 #3 C

13. CLASSWORK – P. 32-33 #3 C

14. SUMMARY
PREPARE FOR QUIZ
p. 15
1. Summarize the mathematics
2. Check your understanding