Chaptus Threeus Reviewus
(Latin for there is a test on Wednesday. Don’t forget about Sketchpad!)
Vocabulary: Skew lines, parallel lines, alternate interior angles, same side interior
angles, corresponding angles, transversal, regular polygon, equilateral, equiangular
Theorems: (These will NOT be given to you on test day)
If Corresponding angles congruent, lines parallel
If Alternate interior angles are congruent, lines parallel
If Same side interior angles are supplementary, lines parallel
If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
2 lines (all coplanar) perpendicular to the same line are parallel.
If lines parallel, Corresponding angles are congruent
If lines parallel Alternate interior angles are congruent
If lines parallel side interior angles are supplementary
If 2 lines are parallel to a third line, then all three lines are parallel to each other.
More Theorems: (More likely to use these to solve equations)
Exterior angle equals the sum of the 2 remote interiors in a triangle
Sum of the inside angles of polygon (n-2)180
Exterior angles of polygon sum to 360
N
4
1
15
3
9
2
5
7
10
6
8
14
12
11
M
J
13
K
16
True or false: If true, give the reason.
If 3  6 , then J // K ______________
If 10  6 , then N // M ______________
If 11, 8 are supplementary, then N // M ______________
If 13  6 , J // K ______________
J
1
3
4
2
5
6
8
7
K
3. Find all of the missing angles that you can with the given information and the picture
above.
a. 8  30, 2  100 , J //K
b. 8  40, 5  60
4. Use the picture
L
B
A
1
3
5
6
2
F
4
M
C
G
D
E
N
a. Let m3  2 x  y , m4  3x  y, 1  30, 2  60 where N // M // L. Solve
for x and y.
b. Given: 4, 5 are supplementary.
Prove: L // M
A
4
B
6
2
4, 1 are supplementary.
Given: AB // FG
Prove: m1  m2  m4
3
5.
5
1
F
G
6. The measure of each interior angle of a regular polygon is 12 more than 6 times
that of an exterior angle. How many sides does the polygon have?
7. In ABC , D is on CB such that mCAD  mCDA . mCAB  mABC  30.
Find mBAD .
a
e
b
d
c
8.
80
f
50
60 g
70
Find the measures of angles a – g.