Download module i vocabulary part iii

MODULE I VOCABULARY
PART III
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.
PARALLEL UNIVERSE
• The reason was talk about congruence is that
we are now beginning our talk of transversals
as they intersect parallel lines.
PARALLEL UNIVERSE
• When two parallel lines are both intersected
by a single line, we say that that line is a
transversal.
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.
PARALLEL UNIVERSE
• Certain things happen when two parallel lines
are intercepted by a transversal.
• Let’s discover a few on our own.
PARALLEL UNIVERSE
• Angles 1 and 2 are called vertical angles.
• What is their relationship?
1
2
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.
PARALLEL UNIVERSE
• Angles 1 and 2 here are called alternate
interior angles.
• What is their relationship?
2
1
PARALLEL UNIVERSE
• Alternate interior angles are angles on
different sides of the transversal and between
the two parallel lines.
• They are always congruent.
PARALLEL UNIVERSE
• Angles 1 and 2 here are called alternate
exterior angles.
• What is their relationship?
1
2
PARALLEL UNIVERSE
• Alternate exterior angles are angles on
different sides of the transversal and outside
of the two parallel lines.
• They are always congruent.
PARALLEL UNIVERSE
• Angles 1 and 2 here are called same-side
interior angles.
• What is their relationship?
2
1
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.
PARALLEL UNIVERSE
• Angles 1 and 2 here are called same-side
exterior angles.
• What is their relationship?
1
2
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.
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 y2 – y1
x2 – x1
𝑟𝑖𝑠𝑒
• This is sometime called
𝑟𝑢𝑛
PARALLEL UNIVERSE
• How do you think the slopes of parallel lines
will relate?
PARALLEL UNIVERSE
• Use the space to find the slope of the two
lines.
PARALLEL UNIVERSE
• Both have a slope of 2/3!
• Parallel lines will always have equal slopes.
• But what about perpendicular lines?
PARALLEL UNIVERSE
• Use the space to find the slope of the two
lines.
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.
PARALLEL UNIVERSE
• If you are ever asked to prove two lines are
parallel or perpendicular, this is how you do it.