Geometry Chapter 3 Review

Geometry Chapter 3 Review PowerPoint PPT Presentation


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Transversals, Lines and their Angle Relationships. . . . 1. 5. 4. 8. 7. 6. 2. 3. Transversal. Alternate Interior Angles - Angles that are on opposite sides of the transversal and inside the parallel lines. Examples: 3

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Geometry Chapter 3 Review

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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

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