1. We will prove1 Lines are Parallel.
LEARNING OBJECTIVE
Definition
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3. ACTIVATE PRIOR KNOWLEDGE
Remember the Concept
Parallel lines have the same slope and will never intersect. 
Perpendicular lines have negative reciprocals slopes of each other, and  intersects at 90 degrees.
Find the equation of the line.
1. The line is parallel to
y = and passes
through the point (−3, −1).
2. The line is perpendicular to
y = and passes through
the point (1, 8).
ACTIVATE PRIOR KNOWLEDGE
Make the Connection
Students you already know how to write equations of a parallel and perpendicular lines, today we will learn how to prove if two lines are parallel using angle theorems we learned in the past.

4. Recall A: What is adjacent, complementary,
Check for Understanding
A: What is adjacent, complementary,
supplementary, & vertical angles?
Check for Understanding
B: What is Acute, Right, Obtuse, and Straight angles?
Recall
CONCEPT DEVELOPMENT

5. There are six ways to prove two lines are parallel. Example
Check for Understanding
Draw and label one of the six ways to prove lines are parallel on whiteboard.
CONCEPT DEVELOPMENT

6. A proof is a logical argument presented with factual statements in order to arrive at a conclusion. Writing a proof is like solving a puzzle or using Legos to create a model of something. Everything needs to fit in an appropriate place.
A two-column proof is one common way to organize a proof in geometry. Two-column proofs always have two columns: one for statements and one for reasons.
A converse of a theorem is a statement formed by interchanging the conclusion with the statement.
CONCEPT DEVELOPMENT
Check for Understanding
A: What is a proof?
B: What is a two-column proof?

7. SKILL DEVELOPMENT / GUIDED PRACTICE
Check for Understanding
A: What are the three steps?
B: What is the reason on line 1? 1
Start with the given information. 2
You must have a reason for EVERY statement. 3
The order of the statements in the proof is not always fixed, but make sure the order makes logical sense.
Remember the Concept
A two-column proof is one common way to organize a proof in geometry. Two- column proofs always have two columns: one for statements and one for reasons.
SKILL DEVELOPMENT / GUIDED PRACTICE
Definition
If the two lines are parallel, the corresponding angles are equal.

8. A: What is Reflexive Property? Give an example.
Check for Understanding
A: What is Reflexive Property? Give an example.
B: What is Symmetric Property? Give an example.

9. A trellis consists of overlapping wooden slats. What must the
value of x be in order for the two slats to be parallel?
Check for Understanding
A: What type of angles are formed in the diagram?
B: How to do you solve for x?
Corresponding angles, therefore,
they must be congruent.
RELEVANCE

10. What did you learn today about proving parallel lines.
Word Bank
Corresponding angles
Alternate angles
Consecutive angles
Same-Side angles
Converse
SUMMARY CLOSURE