Download Geometry 3.1 ‐ Properties of Parallel Lines A. Identifying Angles

Geometry
3.1 ‐ Properties of Parallel Lines
A. Identifying Angles
• Transversal ‐ a line that intersects two coplanar lines at two distinct (separate) points. • Alternate Interior Angles ‐ two interior angles which lie different lines on opposite sides of a transversal.
EXAMPLE: Name several pairs of alternate interior angles.
• Same‐Side Interior Angles ‐ two angles which lie on different lines on the same side of a transversal.
EXAMPLE: Name several pairs of same‐
side interior angles
5 6
2 1
3 4
7 8
• Corresponding Angles ‐ two angles which lie on different lines located in similar positions
EXAMPLE: Name several pairs of corresponding angles
Oct 6­8:57 AM
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B. Examples. Classify each pair of angles as alternate interior, same‐
side interior, or corresponding. Lines are parallel.
1. 2
2.
2
1
1
3.
2
1
Oct 6­9:01 AM
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C. Properties of Parallel Lines
(1) Corresponding Angles Postulate ‐ if a transversal intersects two parallel lines, then the corresponding angles are congruent
t
5 6
l
4 1
3 2
7
m
8
(2) Alternate Interior Angles Theorem ‐ if a transversal intersects two t
parallel lines, then alternate interior angles are congruent.
5 6
l
4 1
3 2
7
m
8
(3) Same‐Side Interior Angles Theorem ‐ If a transversal intersects two parallel lines, then the same‐side interior angles are supplementary
t
5 6
4 1
3 2
7
l
m
8
(4) Alternate Exterior Angles Theorem ‐ if a transversal intersects two parallel lines, then alternate exterior angles are congruent
t
5 6
4 1
3 2
7
l
m
8
(5) Same‐Side Exterior Angles Theorem ‐ if a transversal intersects two parallel lines, then same‐side exterior angles are supplementary. t
5 6
4 1
3 2
7
l
m
8
Oct 6­9:05 AM
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D. Examples. Find the measure of angles 1 and 2. Justify your answer. Lines are parallel.
1. 2.
1
88
0
1
2
1040
2
3.
4.
1
1250
2
1
680
2
Oct 6­9:14 AM
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E. Examples. Find the value of x. Then find the measure of each angle. Lines are parallel.
1. 2. x0
(x ­ 26)0
(3x ­ 5)0
(x + 55)0
Oct 6­9:18 AM
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3.1 HW p. 131 #s 1 ­ 6, 8 ­ 17
Oct 13­8:49 AM
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