- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

**1. **Geometry Chapter 3 Review Parallel Lines & Transversals
Angles and Parallel Lines
Slopes of Lines
Writing Linear Equations
Proving Lines Parallel
Parallels & Distances

**2. **Transversals, Lines and their Angle Relationships

**3. **Angles and Parallel Lines

**4. **Parallel Lines and their Angle Relationships

**6. **1) Solve for each angle

**7. **2) Find each angle measure

**12. **Finding Slopes (m) of lines

**13. **Finding Slopes (m) of lines

**14. **Slopes (m) of Special lines

**18. **Finding Slopes from points

**19. **Find the slope of the following lines

**20. **Slope of Special Lines Parallel lines have equal slopes
Perpendicular lies have slopes that opposite (change sign) and inverses (flip)
Find the slope of line that is parallel to the line through the points (0,7) & (4, 9)
Slope of given line is 2/4 = 1/2, parallel = 1/2
Find the slope of line that is perpendicular to the line through the points (0,7) & (4, 9)
Slope of given line is 2/4 = 1/2, perpendicular = -2

**21. **Writing Equations of Lines

**22. **A line runs through points (3,2) & (-7,5)

**23. **Proving Lines Parallel Postulate 3-4: If two lines is a plane are cut by a transversal so that corresponding angles are congruent, the the lines are parallel.
Parallel Postulate: If there is a line and a point not on the line, then there exists exactly one line through the pint that is parallel to the given line.
Theorem 3-5: If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

**24. **Proving Lines Parallel Theorem 3-6: If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
Theorem 3-7: If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.
Theorem 3-8: In a plane, if two lines are perpendicular to the same line, then they are parallel.

**25. **Find the value of x and angle ABC so that p & q are parallel

**26. **Given the following information, determine which lines are parallel and why.

**27. **Determine the value of x so that a & b are parallel

**28. **Determine the value of x so that a & b are parallel

**29. **Determine the value of x so that a & b are parallel

**30. **Determine the value of x so that a & b are parallel

**31. **Determine the value of x so that a & b are parallel

**32. **Determine the value of x so that a & b are parallel

**33. ** Theorem 3-6 states that if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Write a proof of this theorem using the diagram below. You cannot use the theorem as a reason.

**35. **Parallels and Distances The distance from a line and a point not on the line is the length of the perpendicular segment to the line from the point.
The distance between two parallel lines is the distance between one of the lines and any point on the other line.

**36. **Show the distance between the segments