1. 4.3 – Proving Lines are Parallel
Fill in your notes

2. Recall: Conditional statement: If a, then b.
CONVERSE statement: If b, then a.
For the converse, we just switch the hypothesis and conclusion

3. Ex: If ∠3 ≅ ∠7, then j // k Corresponding Angles Converse -
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Ex: If ∠3 ≅ ∠7, then j // k

4. Ex: If ∠3 ≅ ∠6, then j // k Alternate Interior Angles Converse -
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Ex: If ∠3 ≅ ∠6, then j // k

5. Ex: If ∠1 ≅ ∠8, then j // k Alternate Exterior Angles Converse -
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Ex: If ∠1 ≅ ∠8, then j // k

6. Ex: If m∠3 + m∠5=180°, then j // k
Consecutive (Same-Side) Interior Angles Converse -
If two lines are cut by a transversal so that consecutive (same-side) interior angles are supplementary, then the lines are parallel.
Ex: If m∠3 + m∠5=180°, then j // k

7. Vertical Angles are ≅
Transitive POC
Corresponding Angles CONVERSE

8. Which lines are parallel? Why? **Figures not drawn to scale
= 180
So ∠CHA and ∠DAH are supplementary
CH // AD
Which lines are parallel? Why? **Figures not drawn to scale

9. Which lines are parallel? Why? **Figures not drawn to scale
80°
Linear pair
80 = 80
The two 80° angles are congruent AND corresponding, so…..
l // m
Which lines are parallel? Why? **Figures not drawn to scale

10. Which lines are parallel? Why? **Figures not drawn to scale
50 = 50
∠BAC and ∠DCA are congruent and alternate interior angles
So…
BA // CD
30°
Because a triangle adds to And the 30 and 20 are not equal so BC is not parallel to AD
Which lines are parallel? Why? **Figures not drawn to scale

11. Which lines are parallel? Why? (Try these on your own)
J // k
l // m
none
l // m
J // k
Which lines are parallel? Why? (Try these on your own)

12. The two angles are corresponding angles, so for j//k they have to be congruent (equal)
3x + 5 = 65
3x = 60
x = 20

13. The two angles are consecutive (same-side) interior angles, so for j//k they have to be supplementary
X + 4x = 180
5x = 180
x = 36

14. m // n
n // k
Corresponding angles Theorem
Corresponding angles Theorem
Transitive
Corresponding angles CONVERSE
m // k

15. EXACTLY ONE!