Parallel Lines and Transversals Geometry D – Section 3.1
Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD
Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD
Parallel Lines and Transversals Transversal - When two parallel lines are cut by another line this is called a transversal. Parallel lines t and s are intersected by line j, k and m. Therefore, line j, k and m are a transversal of lines t and s. S
Parallel Lines and Transversals Identifying Angles Exterior angles are on the exterior of the two lines cut by the transversal. The exterior angles are:
Parallel Lines and Transversals Identifying Angles Interior angles are on the interior of the two lines cut by the transversal. The interior angles are:
Parallel Lines and Transversals Identifying Angles - Vertical angles are: When two lines intersect they form two pairs of “opposite” angles called vertical angles. < 1 and < 3 < 2 and < 4 Vertical angles are congruent. Congruent means angles with the same measurement.
Parallel Lines and Transversals Identifying Angles - If the sum of the measures of two angles is 90° the angles are complementary. Angles a and b are complementary. If the sum of the measures of two angles is 180°, they are supplementary. Angles a and b are supplementary.
Parallel Lines and Transversals Identifying Angles Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal. Alternate interior angles are: Alternate interior angles are congruent.
Parallel Lines and Transversals Identifying Angles Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal. Alternate exterior angles are: Alternate exterior angles are congruent.
Parallel Lines and Transversals Identifying Angles Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal. Corresponding angles are: Corresponding angles are congruent.
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2. 2 and 10 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 1.Line r is a transversal of lines p and q. True – Line r intersects both lines in a plane. False - The angles are corresponding angles on transversal p.
4. 1 and 15 are alternate exterior angles and 5 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. False – The angles are vertical angles created by the intersection of q and r. True - The angles are alternate exterior angles on transversal p.
6. 10 and 15 are vertical angles and 12 are alternate interior angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. True – The angles are alternate interior angles on transversal q. False- 10 and 16 are vertical angles
Determine if the statement is true or false. If false, correct the statement and 4 are alternate exterior angles and 14 are corresponding angles. Parallel Lines and Transversals Identifying Angles – Check for Understanding False – The angles are a linear pair, they are supplementary angles. True – The angles are corresponding on transversal s.
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