Chapter 3 Overview Flashcards
parallel lines
coplanar lines that do not not intersect
skew lines
non coplanar lines that are not parallel and do not intersect
parallel planes
planes that do not intersect
transversal
line that intersects 2 or more coplanar lines at distinct points
alternate interior angles
nonadjacent interior angles that lie on opposite sides
of the transversal
same side interior angles
interior angles that lie on the same side of the transversal
corresponding angles
lie on the same side of the transversal and in
corresponding positions
Alternate exterior angles
nonadjacent exterior angles that lie on opposite
sides of the transversal
Postulate 3.1 – Same-Side Interior Angles Postulate
If a transversal intersects 2 parallel lines, then same-side interior angles
are supplementary.
Theorem 3-1 – Alternate Interior Angles Theorem
If a transversal intersects 2 parallel lines, then alternate interior angles
are congruent.
Theorem 3-2 – Corresponding Angles Theorem
If a transversal intersects 2 parallel lines, then corresponding angles are
congruent.
Theorem 3-3 – Alternate Exterior Angles Theorem
If a transversal intersects 2 parallel lines, then alternate interior angles are
congruent.
Theorem 3-4 – Converse of the Corresponding Angles Theorem
If 2 lines and a transversal form corresponding angles that are congruent,
then the lines are parallel.
Theorem 3-5 - Converse of the Alternate Interior Angles Theorem
If 2 lines and a transversal form alternate interior angles that are
congruent, then the 2 lines are parallel.
Theorem 3-6 – Converse of the Same-Side Interior Angles Postulate
If 2 lines and a transversal form same-side interior angles that are
supplementary, then the 2 lines are parallel.
Theorem 3-7 – Converse of the Alternate Exterior Angles Theorem
If 2 lines and a transversal form alternate exterior angles that are
congruent, then the 2 lines are parallel.
Theorem 3-8
If 2 lines are parallel to the same line, then they are parallel to each other.
Theorem 3-9
In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other
Theorem 3-10 – Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is
perpendicular to the other.
Postulate 3-2 – Parallel Postulate
If there is a line and a point not one the line then there is exactly one line through the point parallel to the given line
Theorem 3-11 – Triangle Angle-Sum Theorem
The sum of the measures of the angles
of a triangle is 180.
exterior angle of a polygon
an angle formed by a side and an extension of an
adjacent side
remote interior angles
the 2 nonadjacent interior angles for each exterior
angle
Theorem 3-12 – Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures
of the 2 remote interior angles.
Constructing parallel lines
- Begin with point P and line K
- Draw an arbitrary line through pint P, intersecting line K. Call the intersection point Q.
- Center the compass at point Q and draw an arc intersecting both lines. Without changing the radius of the compass, center it at point P and draw another arc.
- Set the compass radius to the distance between the 2 intersection points of the first arc. Now center the compass at the point where the second arc intersects the line PQ. Mark the arc intersections point R.
Line PR is parallel to line K.
slope
ratio of the vertical change (rise) to the horizontal change (run) between
any two points
slope formula
m = rise / run = y2− y1 / x2 − x1
slope intersept form
y = mx + b where m is the
slope and b is the y-int
point slope form
y - y1 = m(x - x1) where m
is the slope and (x1, y1) is
a pt on the line
Slope of Parallel lines
If 2 nonvertical lines are parallel, then their slopes are equal.
If the slopes of 2 distinct nonvertical lines are equal, then the lines are
parallel.
Any 2 vertical lines or horizontal lines are parallel.
Slope of Perpendicular Lines
If 2 nonvertical lines are ⊥, then the product of their slope is -1.
If the slopes of 2 lines have a product of -1, then the lines are ⊥.
Any horizontal line and vertical line are ⊥.
Postulate 3-3 : Perpendicular Postulate
Through a point not on a line, there is one and only one line perpendicular to
the given line.
