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Parallel and Perpendicular Lines

Parallel and Perpendicular Lines. Information. Conditional statements. A conditional statement has the form “ if x , then y .”. x is called the hypothesis. y is called the conclusion. Name a conditional statement from geometry. The corresponding angles postulate :.

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Parallel and Perpendicular Lines

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  1. Parallel and Perpendicular Lines

  2. Information

  3. Conditional statements A conditional statement has the form “if x, then y.” • x is called the hypothesis. • y is called the conclusion. Name a conditional statement from geometry. The corresponding angles postulate: ...pairs of corresponding angles are congruent. ...two parallel lines are cut by a transversal... If... then... conclusion hypothesis

  4. The converse of a statement The converse of a statement is given by exchanging the hypothesis and conclusion. Find the converse of the corresponding angles postulate. The corresponding angles postulate: ...pairs of corresponding angles are congruent. ...two parallel lines are cut by a transversal... If... then... The converse of thecorresponding angles postulate: ...pairs of corresponding angles are congruent... ...two parallel lines are cut by a transversal. If... then...

  5. Converse of the CAP Converse of the corresponding angles postulate: If two lines are cut by a transversal such that corresponding angles are congruent, then the two lines are parallel. 1 r hypothesis: ∠1 ≅ ∠2 2 conclusion:r‖s s

  6. The parallel postulate How many lines can be drawn that are parallel to s? There is no limit. How many lines can be drawn that are parallel to s and go through point P? There is only one. Parallel postulate: Through a point P not on line s, there is exactly one line parallel to s.

  7. Constructing parallel lines (1)

  8. Proving lines parallel What can you say about the relationship between lines r and s? Prove it. given: ∠1 ≅ ∠2 hypothesis: r‖s vertical angle theorem: ∠1 ≅ ∠3 corresponding angles: ∠2 ≅ ∠3 Since ∠2 is congruentto ∠3 r ‖ s converse of the corresponding angles theorem:  This is the converse of the alternate interior angle theorem.

  9. Converses of the angle theorems

  10. Constructing parallel lines (2)

  11. Constructing perpendicular lines (1)

  12. Constructing perpendicular lines (2)

  13. Shortest distance A lifeguard on the beach sees a child in trouble. Swimming is much slower than running, so how should the lifeguard get to the child in order to minimize the distance she swims to rescue the child? P hint: draw a diagram. Represent the beach as a line and the child and the lifeguard as points. L C The shortest segment from a point to a line is always perpendicular to the line. She should run to point P, then swim to the child to minimize the distance swum.

  14. Constructing perp. bisector (3)

  15. Angles in origami

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