Lesson 3-5Lesson 3-5

Proving Lines Proving Lines ParallelParallel

Ohio Content Standards:

Ohio Content Standards:

Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

Ohio Content Standards:

Solve and graph linear equations and inequalities.

Ohio Content Standards:

Write and use equivalent forms of equations and inequalities in problem situations.

Ohio Content Standards:

Describe and interpret rates of change from graphical and numerical data.

Ohio Content Standards:

Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals.

Postulate 3.4

Postulate 3.4If corresponding angles are congruent, then lines are parallel.

Postulate 3.5

Postulate 3.5If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

Theorem 3.5

Theorem 3.5If alternate exterior angles are congruent, then lines are parallel.

Theorem 3.6

Theorem 3.6If consecutive interior angles are supplementary, then lines are parallel.

Theorem 3.7

Theorem 3.7If alternate interior angles are congruent, then lines are parallel.

Theorem 3.8

Theorem 3.8If two lines are perpendicular to the same line, then lines are parallel.

Determine which lines, if any, are parallel.

Determine which lines, if any, are parallel.

P

100°77°

103°

R

Qb

a

. that so and Find MNPQZYNmx

. that so and Find MNPQZYNmx P

NM

Z

Y

X Q

W(11x - 25)°

(7x + 35)°

Assignment:Assignment:

Pgs. 155-157 Pgs. 155-157 14-30 evens, 14-30 evens, 48-56 evens48-56 evens