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Geometry Notes

Geometry Notes. Sections 3-1. What you’ll learn. How to identify the relationships between two lines or two planes How to name angles formed by a pair of lines and a transversal. Vocabulary. Parallel lines Parallel planes Skew lines Transversal Interior Angles Exterior Angles

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Geometry Notes

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  1. Geometry Notes Sections 3-1

  2. What you’ll learn • How to identify the relationships between two lines or two planes • How to name angles formed by a pair of lines and a transversal

  3. Vocabulary • Parallel lines • Parallel planes • Skew lines • Transversal • Interior Angles • Exterior Angles • Consecutive (same – side ) Interior Angles • Alternate Interior Angles • Alternate Exterior Angles • Corresponding Angles

  4. RELATIONSHIPS BETWEEN LINES 2 Lines are either Coplanar Noncoplanar INTERSECTING LINES(The lines intersect once) SKEW lines are two noncoplanar lines that never intersect PARALLEL LINES(The lines never intersect) This is what we’ll study in Chapter 3 COINCIDENT LINES(The lines intersect at all points)

  5. Let’s start with any 2 coplanar lines • Any line that intersects two coplanar lines at two different points is called a transversal 2 1 4 3 transversal 6 • 8 angles are created by two lines and a transversal 5 8 7 • 4 Interior Angles • 3, 4, 5, 6 • 4 Exterior Angles • 1, 2, 7, 8

  6. Consecutive Interior Angles 2 • We have two pairs of interior angles on the same side of the transversal called Consecutive Interior Angles or same-side interior angles 1 4 3 6 5 8 7 • The two pairs of consecutive (same-side) interior: • 3 &5 • 4 & 6

  7. Alternate Interior Angles • We have two pairs of interior angle on opposite sides of the transversal called Alternate Interior Angles 2 1 4 3 Alternate Interior Angles 6 5 8 7 • The two pairs of alternate interior angles are: • 3 &6 • 4 & 5

  8. Alternate Exterior Angles • We have two pairs of exterior angles on opposite sides of the transversal called Alternate Exterior Angles 2 1 4 3 6 5 8 7 • The two pairs of Alternate Exterior Angles • 1 & 8 and 7 & 2

  9. Corresponding Angles • Corresponding Angles are in the same relative position 2 1 4 3 6 5 8 7 • There are four pairs of Corresponding Angles • 1 & 5, 2 & 6, 3 & 7, and 4 & 8

  10. Find an example of each term. • Corresponding angles • Alternate exterior angles • Linear pair of angles • Alternate interior angles • Vertical angles

  11. Now if the lines are parallel. . . • The corresponding angles postulate (remember these are true without question)says. . . • All kinds of special things happen. . . • If two parallel lines are cut by a transversal, then the corresponding angles are congruent. • The four pairs of Corresponding Angles are  • 1  5 • 2  6 • 3  7 • 4  8 2 1 4 3 6 5 8 7

  12. Tell whether each statement is always (A), sometimes (S), or never (N) true. • 2 and 6 are supplementary • 1  3 • m1 ≠m6 • 3  8 • 7 and 8 are supplementary • m5 =m4

  13. Find each angle measure.

  14. Find each angle measure.

  15. Find each angle measure.

  16. Determine whether or not l1║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

  17. Determine whether or not l1║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

  18. Determine whether or not l1║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

  19. Have you learned .. . . • How to identify the relationships between two lines or two planes • How to name angles formed by a pair of lines and a transversal • Assignment: Worksheet 3.1

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