Homework Review

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Homework Review
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CCGPS Analytic GeometryDay 3 (1/13/14)
UNIT QUESTION How do I prove geometric theorems
involving lines, angles, triangles and
parallelograms? Standards MCC9-12.G.SRT.1-5,
MCC9-12.A.CO.6-13 Todays Question Which angles
are congruent to each other when parallel lines
are cut by a transversal? Standard
MCC9-12.A.CO.9
3
Parallel Lines and Transversals
4
Parallel Lines Two lines are parallel if and
only if they are in the same plane and do not
intersect.
B
A
D
C
AB ??CD
5
Parallel Planes Planes that do not intersect.
6
Skew Lines two lines that are NOT in the same
plane and do NOT intersect
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Ex 1 Name all the parts of the prism shown
below. Assume segments that look parallel are
parallel.
1. A plane parallel to plane AFE.
F
E
Plane BGD
G
D
2. All segments that intersect GB.
A
C
B
GD, BC
3. All segments parallel to FE.
4. All segments skew to ED.
BG, FA, BC
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Transversal A line, line segment, or ray that
intersects two or more lines at different points.
a
b
Line t is a transversal.
t
9
Special Angles
2
1
4
Interior Angles lie between the two lines (?3,
?4, ?5, and ?6)
3
6
5
8
7
Alternate Interior Angles are on opposite sides
of the transversal. (?3 ?6 AND ?4 and ?5)
Consecutive Interior Angles are on the same
side of the transversal. (?3 ?5 AND ?4 ?6)
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More Special Angles
Exterior Angles lie outside the two lines (?1,
?2, ?7, and ?8)
2
1
4
3
6
5
8
7
Alternate Exterior Angles are on opposite sides
of the transversal (?1 ?8 AND ?2 ?7)
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Ex. 2 Identify each pair of angles as alternate
interior, alternate exterior, consecutive
interior, or vertical.
a. ?1 and ?2
1
Alt. Ext. Angles
6
7
3
b. ?6 and ?7
4
8
5
Vertical Angles
2
c. ?3 and ?4
Alt. Int. Angles
d. ?3 and ?8
Consec. Int. Angles
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Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal,
then each pair of alternate interior angles are
congruent.
8
1
7
?2 ? ?6
2
6
3
5
4
?3 ? ?7
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Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal,
then each pair of alternate exterior angles are
congruent.
8
1
7
?1 ? ?5
2
6
3
5
4
?4 ? ?8
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Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal,
then each pair of consecutive interior angles are
supplementary.
m?2 m?3 180
8
1
7
2
6
m?6 m?7 180
3
5
4
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Ex. 3 In the figure, p??q. If m?5 28, find
the measure of each angle.
28
a. m?8
q
2
1
p
b. m?1
28
4
3
c. m?2
152
6
5
8
7
d. m?3
152
e. m?4
28
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Ex. 4 In the figure, s??t. Find the m?CBG.
t
A
Step 1 Solve for x.
G
S
B
D
3x 5 4x - 29
3x -5
C
-5 x - 29
4x -29
E
24 x
F
Step 2 m?CBG m?ABE 3x -5.
3x-5 3(24) 5 72-5 67
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Ex 5 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
alternate exterior
8
1
15
13
7
2
6
14
3
5
4
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Ex 6 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
consecutive interior
8
1
15
13
7
2
6
14
3
5
4
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Ex 7 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
alternate interior
8
1
15
13
7
2
6
14
3
5
4
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Ex 8 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
alternate exterior
8
1
15
13
7
2
6
14
3
5
4
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Ex 9 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
consecutive interior
8
1
15
13
7
2
6
14
3
5
4
22
Ex 10 Identify each pair of angles as alt.
interior, alt. exterior, consecutive interior, or
vertical.
10
11
9
12
16
vertical
8
1
15
13
7
2
6
14
3
5
4