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Do Now A B C D 1.Name a line that does not intersect with line AC. 2.What is the intersection of lines AB and DB?
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3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals Objective: To identify angle pairs formed by three intersecting lines; to use angles formed by parallel lines and transversals
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Parallel Lines Lines that do not Intersect and are coplanar
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Parallel Planes Planes that Do not Intersect
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Skew Lines Lines that do Not intersect and are not Coplanar.
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Transversal Transversal: a line that intersects two or more coplanar lines.
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Angles formed by a transversal There are 4 types of angles formed by a transversal.
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Corresponding angles 1 5 Angles 1 and 5 are corresponding Because they have corresponding Positions.
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Corresponding angles of Parallel Lines 1 5 The corresponding angles 1 and 5 Are congruent to each other Because lines k and m are parallel To each other. k m
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Alternate Exterior Angles 1 Angles 1 and 8 are alternate Exterior angles because they are On alternate sides of the Transversal and are exterior Of the two lines. 8
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Alternate Exterior angles of Parallel Lines 1 The alternate exterior angles 1 and 8 are congruent to each other because lines k and m are Parallel to each other. k m 8
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Alternate Interior Angles Angles 3 and 6 are alternate interior angles because they are On alternate sides of the Transversal and on the interior Of the two lines. 3 6
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Alternate Interior angles of Parallel Lines The alternate interior angles 3 and 6 are congruent to each other because lines k and m are Parallel to each other. k m 6 3
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Consecutive Interior Angles Angles 4 and 6 are consecutive Interior angles because they are On the same side of the transversal And are inside the two lines. 4 6
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Consecutive Interior angles of Parallel Lines The consecutive interior angles 4 and 6 are supplementary to each other because lines k and m are parallel to each other. k m 6 4
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Parallel lines cut by a transversal. When two parallel lines are cut by a transversal the following relationships are true. –Corresponding angles are congruent –Alternate exterior angles are congruent –Alternate interior angles are congruent –Consecutive interior angles are supplementary.
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Example 1: 1 5 Name all pairs of corrsponding, alternate interior, alternate exterior, and consecutive interior angles. 2 3 4 6 78
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Example: Classify the angle pair x y
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m n
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p q
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Example 2: Solve for the variable 2p 120
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Example 3: Solve for the variable x 80
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Example 4: Find all the missing angle measures 105
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