MODULE I VOCABULARYPART III

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• 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.

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

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

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• 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.

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• Certain things happen when two parallel lines are intercepted by a transversal.

• Let’s discover a few on our own.

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

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• 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.

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• Angles 1 and 2 here are called alternate interior angles.

• What is their relationship?

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• Alternate interior angles are angles on different sides of the transversal and between the two parallel lines.

• They are always congruent.

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• Angles 1 and 2 here are called alternate exterior angles.

• What is their relationship?

1

2

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• Alternate exterior angles are angles on different sides of the transversal and outside of the two parallel lines.

• They are always congruent.

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• Angles 1 and 2 here are called same-side interior angles.

• What is their relationship?

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• Same-side interior angles are angles on the same side of the transversal and inside the two parallel lines.

• They are always supplementary.

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• Angles 1 and 2 here are called same-side exterior angles.

• What is their relationship?

1

2

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• Same-side exterior angles are angles on the same side of the transversal and outside the two parallel lines.

• They are always supplementary.

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• 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

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• How do you think the slopes of parallel lines will relate?

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• Use the space to find the slope of the two lines.

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• Both have a slope of 2/3!• Parallel lines will always have equal slopes.• But what about perpendicular lines?

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• Use the space to find the slope of the two lines.

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• 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.

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