1. birds four-footed mammals dogs poodles
Using the diagram below, complete these sentences:
_____________ are always ______________.
______________ are sometimes ________________.
_____________ are never ______________.
birds
four-footed mammals
dogs
poodles

2. Proving Lines are Parallel
Mod 14.3:
Proving Lines are Parallel
Essential Question: How can you prove that two lines are parallel?
CASS: G-CO.9 Prove theorems about lines and angles.
MP.3 Logic

3. Conditional Statements
Venn Diagram
Read “if p then q”
Symbols: p  q
Example:
If parallel lines are cut by a transversal, then its alternate int. angles are congruent.
Conclusion
“q”
Hypothesis
“p”
Conclusion
“alt. int. angles congruent”
Hypothesis
“parallel lines°”

4. Converse
Converse of a conditional statement is formed by switching the hypothesis and conclusion.
Conditional Statements: if “p”  then “q”
Converse: if “q”  then “p”

5. Write the converse of the conditional statement
Conditional Statement (p  q):
If parallel lines are cut by a transversal, then its alternate interior angles are congruent.
Converse (q  p):
If alternate interior angles are congruent, then the lines are parallel.

6. SAME SIDE INTERIOR ANGLES CONVERSE POSTULATE
If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
If , 1 2
then j ‖ k.

7. CORRESPONDING ANGLES CONVERSE THEOREM
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
j ‖ k

8. ALTERNATE INTERIOR ANGLES CONVERSE THEOREM
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
If , then j ‖ k 1 3
ALTERNATE EXTERIOR ANGLES CONVERSE THEOREM 1 8
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
If , then j ‖ k

9. Find the value of x that make m || n.
EXAMPLE 1 m n
Find the value of x that make m || n.
Alt. Int. Angles Converse

10. Find the value of x that makes a || b.
TRY THIS a b
Find the value of x that makes a || b.
Cons. Int. Angles Converse

11. 14.3 key question:
How can we prove
two lines are parallel?

12. pp. 705 #1, 3, 5-10 all Key Vocab: ASSIGNMENTS Parallel Lines
Transversal
Same Side Interior Angles Converse
Corresponding Angles Converse
Alternate Interior Angles Converse

14. TICKET-OUT-THE-DOOR
Suppose m∠6 = 83°. Find measure of all the other angles. 1 2 4 3 7 8 6 5
What is the relationship between angles 1 and 7?
What is the relationship between angles 4 and 8?
What is the relationship between angles 3 and 8?