Chapter 3 Overview

Question 1

parallel lines

Answer 1

coplanar lines that do not not intersect

Question 2

skew lines

Answer 2

non coplanar lines that are not parallel and do not intersect

Question 3

parallel planes

Answer 3

planes that do not intersect

Question 4

transversal

Answer 4

line that intersects 2 or more coplanar lines at distinct points

Question 5

alternate interior angles

Answer 5

nonadjacent interior angles that lie on opposite sides

of the transversal

Question 6

same side interior angles

Answer 6

interior angles that lie on the same side of the transversal

Question 7

corresponding angles

Answer 7

lie on the same side of the transversal and in

corresponding positions

Question 8

Alternate exterior angles

Answer 8

nonadjacent exterior angles that lie on opposite

sides of the transversal

Question 9

Postulate 3.1 – Same-Side Interior Angles Postulate

Answer 9

If a transversal intersects 2 parallel lines, then same-side interior angles
are supplementary.

Question 10

Theorem 3-1 – Alternate Interior Angles Theorem

Answer 10

If a transversal intersects 2 parallel lines, then alternate interior angles
are congruent.

Question 11

Theorem 3-2 – Corresponding Angles Theorem

Answer 11

If a transversal intersects 2 parallel lines, then corresponding angles are
congruent.

Question 12

Theorem 3-3 – Alternate Exterior Angles Theorem

Answer 12

If a transversal intersects 2 parallel lines, then alternate interior angles are
congruent.

Question 13

Theorem 3-4 – Converse of the Corresponding Angles Theorem

Answer 13

If 2 lines and a transversal form corresponding angles that are congruent,
then the lines are parallel.

Question 14

Theorem 3-5 - Converse of the Alternate Interior Angles Theorem

Answer 14

If 2 lines and a transversal form alternate interior angles that are
congruent, then the 2 lines are parallel.

Question 15

Theorem 3-6 – Converse of the Same-Side Interior Angles Postulate

Answer 15

If 2 lines and a transversal form same-side interior angles that are
supplementary, then the 2 lines are parallel.

Question 16

Theorem 3-7 – Converse of the Alternate Exterior Angles Theorem

Answer 16

If 2 lines and a transversal form alternate exterior angles that are
congruent, then the 2 lines are parallel.

Question 17

Theorem 3-8

Answer 17

If 2 lines are parallel to the same line, then they are parallel to each other.

Question 18

Theorem 3-9

Answer 18

In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other

Question 19

Theorem 3-10 – Perpendicular Transversal Theorem

Answer 19

In a plane, if a line is perpendicular to one of two parallel lines, then it is
perpendicular to the other.

Question 20

Postulate 3-2 – Parallel Postulate

Answer 20

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

Question 21

Theorem 3-11 – Triangle Angle-Sum Theorem

Answer 21

The sum of the measures of the angles

of a triangle is 180.

Question 22

exterior angle of a polygon

Answer 22

an angle formed by a side and an extension of an

adjacent side

Question 23

remote interior angles

Answer 23

the 2 nonadjacent interior angles for each exterior

angle

Question 24

Theorem 3-12 – Triangle Exterior Angle Theorem

Answer 24

The measure of each exterior angle of a triangle equals the sum of the measures
of the 2 remote interior angles.

Question 25

Constructing parallel lines

Answer 25

1. Begin with point P and line K 2. Draw an arbitrary line through pint P, intersecting line K. Call the intersection point Q. 3. 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. 4. 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.

Question 26

slope

Answer 26

ratio of the vertical change (rise) to the horizontal change (run) between any two points

Question 27

slope formula

Answer 27

m = rise / run = y2− y1 / x2 − x1

Question 28

slope intersept form

Answer 28

y = mx + b where m is the | slope and b is the y-int

Question 29

point slope form

Answer 29

y - y1 = m(x - x1) where m is the slope and (x1, y1) is a pt on the line

Question 30

Slope of Parallel lines

Answer 30

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.

Question 31

Slope of Perpendicular Lines

Answer 31

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 ⊥.

Question 32

Postulate 3-3 : Perpendicular Postulate

Answer 32

Through a point not on a line, there is one and only one line perpendicular to the given line.