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Section 3.1 Lines and Angles. Perpendicular Lines. Intersecting lines that form right angles Symbol. XS SR. Parallel Lines. Two lines that are coplanar and do not intersect Symbol: II. XY II UZ. Skew Lines. Lines do not intersect and are not coplanar. Example. - PowerPoint PPT Presentation
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Section 3.1 Lines and Angles
Perpendicular Lines• Intersecting lines that form right angles
• Symbol
T
XS SR
Parallel Lines• Two lines that are coplanar and do not
intersect
• Symbol: II
T
XY II UZ
Skew Lines• Lines do not intersect and are not coplanar
T
Example
• Is XY parallel or skew to RV?
T
XY II RV
Parallel planes• Two planes that do not intersect
T
Parallel Postulate
• If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Perpendicular Postulate
• If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Theorem 3.1
• If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular
• Ex 1
A B C
D
m<ABD = m<DBC and a linear pair, BD AC
Theorem 3.2
• If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
• Ex. 2
H
F
G
J
<FGJ is complementary to <JGH
Examples: Solve for x
Ex 3.
60°x
ANSWER: 60 + x = 90
-60 -60
x = 30
Example 4
x55°
ANSWER: x + 55 = 90
-55 -55
x = 35
Example 5
27°
(2x-9)°
ANSWER: 2x – 9 + 27 = 90
2x +18 = 90
2x = 72
x = 36
Theorem 3.3
• If 2 lines are perpendicular, then they intersect to form four right angles.
m
l
Complete Try it! Problems
#1-8
Transversal• A line that intersects two or more coplanar
lines at different points.
transversal
Vertical Angles
• Formed by the intersection of two pairs of opposite rays
1 2
3 4
5 6
7 8
Linear Pair
• Adjacent angles that are supplementary
1 2
3 4
5 6
7 8
Corresponding Angles
• Occupy corresponding positions.
1 2
3 4
5 6
7 8
Alternate Exterior Angles
• Lie outside the 2 lines on opposite sides of the transversal.
1 2
3 4
5 6
7 8
Alternate Interior Angles• Lie between the 2 lines on opposite sides
of the transversal.
1 2
3 4
5 6
7 8
Consecutive Interior Angles(Same side interior angles)
• Lie between the 2 lines on the same side of the transversal.
1 2
3 4
5 6
7 8
Angle Relationships: Name a pair of angles
• Corresponding– Ex. 1 & 5
• Alternate Exterior – Ex. 2 & 7
• Alternate Interior– Ex. 4 & 5
• Consecutive Interior– Ex. 3 & 5
1 23 4
5 6
7 8
