Finish Wksht
m<A = 55°
m<B = 35°
x = 10
y = 19
Finish Wksht
x = 90
x = 108
y = 93
y = 36
z = 15
z = 30
If lines are parallel, then:
-----
corresponding angles are ____________.
alternate interior angles are ____________.
alternate exterior angles are ____________.
same-side interior angles are _____________.
Hw Solutions
p. 366-67 # 1-13, 18-27
1. 1 & 2; corr
3 & 4; alt int
5 & 6; corr
2. 1 & 2; same­side int
3 & 4; corr
5 & 6; corr
3. 1 & 2; corr
3 & 4; same­side int
5 & 6; alt int
4. if ll lines, then corr <s congruent.
if ll lines, then same side int <s supp.
5. if ll lines, then corr <s congruent. if ll lines, then same side int <s supp.
6. if ll lines, then same side int <s supp. if ll lines, then alt int <s are congruent.
7. if ll lines, then same side int <s supp. if ll lines, then same side int <s supp.
8. if ll lines, then corr <s congruent.
9. if ll lines, then alt int <s are congruent.
10. if ll lines, then same side int <s supp.
11. if ll lines, then alt int <s are congruent.
12. if ll lines, then corr <s congruent.
13. if ll lines, then corr <s congruent.
18. a. 68° b. 138°
19. 1&9, 2&10, 5&11, 6&12
20. 2&7, 3&6
21. same side int , l
22. corr, p
23. alt int, l 24. corr, l
25. 3, 9
26. 8, 12
27. 7,10
HW Solutions
7­2 Proving Lines Parallel
Objective: Recognize conditions that result in parallel lines.
So far, we know:
If lines are parallel, then:
-- corresponding angles are congruent.
-- alternate interior angles are congruent.
-- alternate exterior angles are congruent.
-- same-side interior angles are supplementary.
We can use these special pairs of angles to show or prove
that lines are parallel.
(like going in reverse)
Converse
Statement:
If the cat will run, then the dog will chase the cat.
Converse:
If the dog will chase the cat, then the cat will run.
If lines are parallel, then alternate
interior angles are congruent.
If alternate interior angles are congruent,
then lines are parallel.
The converse is also true:
If a pair of:
-- corresponding angles are congruent
OR
-- alternate interior angles are congruent
OR
-- alternate exterior angles are congruent
OR
-- same-side interior angles are supplementary
THEN, the lines are parallel !!!
Examples:
Are these lines parallel
by the given information?
If so what postulate proves it?
1. < 1 = < 5
2. < 2 = < 7
HW # 78
Prac 7-1 (#1-9, 13-18)
Prac 7-2 (#1-5,11-16)
** Quiz on Thursday!