Parallel Lines and Transversals Geometry D Section 3

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. S 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.

Parallel Lines and Transversals Identifying Angles - 1 3 2 4 5 7 6 8 Exterior angles are on the exterior of the two lines cut by the transversal. The exterior angles are:

Parallel Lines and Transversals Identifying Angles - 1 3 2 4 5 7 6 8 Interior angles are on the interior of the two lines cut by the transversal. The interior angles are:

Parallel Lines and Transversals Identifying Angles When two lines intersect they form two pairs of “opposite” angles called vertical angles. Vertical angles are congruent. Vertical angles are: Congruent means angles with the same measurement. < 1 and < 3 < 2 and < 4

Parallel Lines and Transversals Identifying Angles - If the sum of the measures of two angles is 90° the angles are complementary. If the sum of the measures of two angles is 180°, they are supplementary. Angles a and b are complementary. Angles a and b are supplementary.

Parallel Lines and Transversals Identifying Angles - 1 3 2 4 5 7 6 8 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 - 1 3 2 4 5 7 6 8 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 - 1 3 2 4 5 7 6 8 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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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 4 3 both lines in a plane. 2 1 5 6 8 7 2. 2 and 10 are alternate interior angles. 9 10 False - The angles are 11 12 16 15 14 13 corresponding angles on transversal p.

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 3. 3 and 5 are alternate interior angles. 1 2 8 7 3 4 6 5 9 10 11 12 16 15 14 13 False – The angles are vertical angles created by the intersection of q and r. 4. 1 and 15 are alternate exterior angles. True - The angles are alternate exterior angles on transversal p.

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 5. 6 and 12 are alternate interior angles. 1 2 8 7 True – The angles are alternate interior angles on transversal q. 3 4 6 5 9 10 11 12 16 15 14 13 6. 10 and 15 are vertical angles. False- 10 and 16 are vertical angles

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 7. 3 and 4 are alternate exterior angles. 1 2 8 7 9 10 False – The angles are a linear pair, they are supplementary angles. 3 4 6 5 11 12 16 15 14 13 8. 16 and 14 are corresponding angles. True – The angles are corresponding on transversal s.

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