Parallel Lines and Angles
Chapter 3
Standardized Test Prep answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
B
G
A
G
C
H
A
G
C
I
C
D
B
B
B
6.32
45
18. a. (6, 2)
19.
b. 10
Proving Lines parallel
 Corresponding Angles Postulate
 If two lines are parallel then corresponding angles
formed by them are congruent
 Alternate Interior Angles Theorem
 If two lines are parallel then alternate interior angles
formed by them are congruent
 Same-Side Interior Angles Theorem
 If two lines are parallel then same-side interior angles
formed by them are supplementary
Answers: 3-1 #10-36
10. a. def. perp. lines
b.
c.
d.
e.
f.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Def. of rt. <
Corr <‘s are congruent
Subst.
Def. of rt. <
Def of perp. Lines
75, 105 corr, ssi
120, 60 corr, ssi
100, 70 ssi, alt. int.
70, 70, 110
25, 65, 65
20, 100, 80
52, 128
One angle
2
20. 4
21. 2
22. 4
23. 32
24. X = 76, y = 37, v = 42, w = 25
25. X = 135, y = 45
26. Discuss
27. Trans means across
28. Discuss
29. Alt. int. are congruent
30. 57, ssi
31. Same-side ext. are
supp….discuss
32. m<1= m<2 v.a. congruent
33. Never
34. Sometimes
35. Sometimes
36. sometimes
Converses of the parallel lines
conjectures
 If corresponding angles are congruent then
the lines must be parallel
 If alternate interior angles are congruent then
the lines must be parallel
 If same side interior angles are
supplementary then the lines must be
parallel.
Starter: Parallel & Perpendicular lines
 If two lines are parallel to the same line then
they are parallel to eachother
WRITE A PROOF
 If two lines in a plane are perpendicular to the
same line, then they are parallel to eachother.
WRITE A PROOF
Think/Pair share:
What is a polygon?
List all characteristics you believe make
something a polygon and anything you
already know about polygons.
Polygons
 Convex vs. non-convex (concave)
Formulas work for convex polygons only
 Regular polygon
Equilateral and equiangular
 Interior Angle Sum
(n-2)*180
 Exterior Angle Sum
360
Constructing an arch
According to legend
when the Romans
made an arch, they
would make the
architect stand under
it while the wooden
support was
removed. That was
one way to be sure
that architects
carefully designed
arches that wouldn't
fall!
Arch intro: Brainstorm
 What shape do you think the blocks could be?
 Look at the interior of the arch.
Sketch it in 2-D.
 How many blocks would we need if our class were
to build an arch?
STARTER: Test Next Block
1. What can you conclude about the bisector of
an exterior angle in a triangle if the remote
interior angles are congruent? Write a proof
to justify your response.
2. HW Peer edit (answers on next slide)
Chapter Test
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
19.
21.
22.
23.
28.
65 corr; 65 V.A
85 AI; 110 SSI
85 corr; 95 SSI
70 corr; 110 SSI
Yes
Yes
No
No
5
25
6
75
given, corr <‘s are congruent, given, transitive property, converse of
corresponding <‘s postulate
Discuss
109
85, 100, 100
30
MINLESSON REQUESTS
SIGN UP FOR THE FOLLOWING:
 Parallel lines & triangle sum theorem problems
 Converse of parallel lines theorems & problems
 Theorems, Postulates & Proofs
 Polygon Angle Sums
TODAY
 Scan Chapter Review www.phsuccessnet.com
 Test Review practice problems/proofs
handout
 Work on Polygon Arch project
design
build block
Keep track of what you completed today on a blank
sheet of paper. Anything not completed must be
done for homework. Test & arch building next block.