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MODULE I VOCABULARY

PART III. MODULE I VOCABULARY. PARALLEL UNIVERSE. When two numbers are the same in mathematics, we say they are equal. When two figures in mathematics are exactly the same, we say they are congruent.

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MODULE I VOCABULARY

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  1. PART III MODULE I VOCABULARY

  2. PARALLEL UNIVERSE • When two numbers are the same in mathematics, we say they are equal. • When two figures in mathematics are exactly the same, we say they are congruent. • Technically, congruent means to have the same size and shape with all angles and sides equal.

  3. PARALLEL UNIVERSE • The reason was talk about congruence is that we are now beginning our talk of transversals as they intersect parallel lines.

  4. PARALLEL UNIVERSE • When two parallel lines are both intersected by a single line, we say that that line is a transversal.

  5. PARALLEL UNIVERSE • When a line segment is intersected so that it creates a right angle, you’ll recall that we call the two lines perpendicular. • Well, when they intersect to form right angles AND the segment is intersected in the center we say that it is a perpendicular bisector.

  6. PARALLEL UNIVERSE • Certain things happen when two parallel lines are intercepted by a transversal. • Let’s discover a few on our own.

  7. PARALLEL UNIVERSE • Angles 1 and 2 are called vertical angles. • What is their relationship? 1 2

  8. PARALLEL UNIVERSE • Vertical angles are angles between a pair of intersecting lines. • Basically, they are the angles that are across from each other. • They are always congruent.

  9. PARALLEL UNIVERSE • Angles 1 and 2 here are called alternate interior angles. • What is their relationship? 1 2

  10. PARALLEL UNIVERSE • Alternate interior angles are angles on different sides of the transversal and between the two parallel lines. • They are always congruent.

  11. PARALLEL UNIVERSE • Angles 1 and 2 here are called alternate exterior angles. • What is their relationship? 1 2

  12. PARALLEL UNIVERSE • Alternate exterior angles are angles on different sides of the transversal and outside of the two parallel lines. • They are always congruent.

  13. PARALLEL UNIVERSE • Angles 1 and 2 here are called same-side interior angles. • What is their relationship? 1 2

  14. PARALLEL UNIVERSE • Same-side interior angles are angles on the same side of the transversal and inside the two parallel lines. • They are always supplementary.

  15. PARALLEL UNIVERSE • Angles 1 and 2 here are called same-side exterior angles. • What is their relationship? 1 2

  16. PARALLEL UNIVERSE • Same-side exterior angles are angles on the same side of the transversal and outside the two parallel lines. • They are always supplementary.

  17. PARALLEL UNIVERSE • Lastly today, we’ll discuss the relationship of the slopes of perpendicular and parallel lines. • Recall that slope between two points is calculated by • This is sometime called

  18. PARALLEL UNIVERSE • How do you think the slopes of parallel lines will relate?

  19. PARALLEL UNIVERSE • Use the space to find the slope of the two lines.

  20. PARALLEL UNIVERSE • Both have a slope of 2/3! • Parallel lines will always have equal slopes. • But what aboutperpendicular lines?

  21. PARALLEL UNIVERSE • Use the space to find the slope of the two lines.

  22. PARALLEL UNIVERSE • One has a slope of 2/3 while the other has a slope of -3/2. • This is what we call an opposite reciprocal. • This is the relationship of the slopes of perpendicular lines.

  23. PARALLEL UNIVERSE • If you are ever asked to prove two lines are parallel or perpendicular, this is how you do it.

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