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Geometry Notes
Sections 3-1
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What you’ll learn
How to identify the relationships between two lines or two planes
How to name angles formed by a pair of lines and a transversal
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Vocabulary Parallel lines Parallel planes Skew lines Transversal Interior Angles Exterior Angles Consecutive (same – side ) Interior Angles Alternate Interior Angles Alternate Exterior Angles Corresponding Angles
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RELATIONSHIPS BETWEEN LINES
2 Lines are either Coplanar Noncoplanar
Two noncoplanar lines that never intersect are called SKEW lines.
The lines intersect once(INTERSECTING LINES)
The lines never intersect(PARALLEL LINES)
The lines intersect at all pts(COINCIDENT LINES)
This is what we’ll study in
Chapter 3
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Let’s start with any 2 coplanar lines Any line that
intersects two coplanar lines at two different points is called a transversaltransversal
8 angles are created by two lines and a transversal
12
34
5 6
7 8
4 Interior Angles 3, 4, 5, 6
4 Exterior Angles 1, 2, 7, 8
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12
34
5 6
7 8
Consecutive Interior Angles We have two pairs
of interior angles on the same side of the transversal called Consecutive Interior Angles or same-side interior angles
The two pairs of consecutive (same-side) interior: 3 &5 and 4 & 6
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Alternate
We have two pairs of interior angle on opposite sides of the transversal called Alternate Interior Angles
12
34
5 6
7 8
Alternate Interior Angles
InteriorAngles
The two pairs of alternate interior angles are: 3 &6 and 4 & 5
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Alternate Exterior Angles
12
34
5 6
7 8
The two pairs of Alternate Exterior Angles 1 & 8 and 7 & 2
We have two pairs of exterior angles on opposite sides of the transversal called Alternate Exterior Angles
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1
Corresponding Angles
2
34
5 6
7 8
There are four pairs of Corresponding Angles 1 & 5, 2 & 6, 3 & 7, and 4 & 8
Corresponding Angles are in the same relative position
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Find an example of each term. Corresponding
angles Alternate exterior
angles Linear pair of
angles Alternate interior
angles Vertical angles
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Now if the lines are parallel. . . All kinds of special things happen. . . The corresponding angles postulate (remember these are
true without question) says. . .
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
12
3 4
5 6
7 8
The four pairs of Corresponding Angles are
1 5 2 6 3 7 4 8
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Tell whether each statement is always (A), sometimes (S), or never (N) true. 2 and 6 are
supplementary 1 3 m1 ≠ m6 3 8 7 and 8 are
supplementary m5 = m4
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Find each angle measure.
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Find each angle measure.
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Find each angle measure.
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Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”
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Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”
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Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”
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Have you learned .. . .
How to identify the relationships between two lines or two planes
How to name angles formed by a pair of lines and a transversal
Assignment: Worksheet 3.1