Unit 3: Parallel Lines & Planes

Question 1

parallel lines

Answer 1

coplanar lines that do not intersect

Question 2

skew lines

Answer 2

noncoplanar lines that are neither parallel nor intersecting

Question 3

parallel planes

Answer 3

planes that do not intersect

Question 4

when are a line and a plane parallel?

Answer 4

when they don’t intersect

Question 5

a plane intersecting 2 parallel planes

Answer 5

if 2 parallel planes are cut by a third plane, then the lines of intersection are parallel

Question 6

transversal

Answer 6

a line that intersects 2+ coplanar lines in different points

Question 7

alternate interior angles

Answer 7

2 nonadjacent interior angles on opposite sides of the transversal

Question 8

same side interior angles

Answer 8

2 interior angles on the same side of the transversal

Question 9

corresponding angles

Answer 9

2 angles in corresponding positions relative to the 2 lines

Question 10

corresponding angles postulate

Answer 10

if 2 lines are cut by a transversal, then the corresponding angles are congruent

Question 11

alternate interior angles theorem

Answer 11

if 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent

Question 12

same side interior angles theorem

Answer 12

if 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary

Question 13

perpendicular transversal theorem

Answer 13

if a transversal is perpendicular to 1 of 2 parallel lines, then it is also perpendicular to the other line as well

Question 14

corresponding angles theorem converse

Answer 14

if a transversal cuts 2 lines such that the corresponding angles are congruent, then the 2 lines are parallel

Question 15

alternate interior angles theorem converse

Answer 15

if 2 lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel

Question 16

same side interior angles theorem converse

Answer 16

if 2 lines are cut by a transversal and the same side interior angles are supplementary angles, then the lines are parallel

Question 17

perpendicular transversal theorem converse

Answer 17

in a plane, 2 lines perpendicular to the same line are also parallel

Question 18

parallel postulate

Answer 18

through a point outside a line, there is exactly 1 line parallel to the given line

Question 19

perpendicular postulate

Answer 19

through a point outside a line, there is exactly 1 line perpendicular to the given line

Question 20

parallel lines transitivity theorem

Answer 20

2 lines parallel to a third line are parallel to each other

Question 21

triangle sum theorem

Answer 21

the sum of the measures of a triangle ins 180

Question 22

triangle sum corollaries

Answer 22

1. if 2 angles of 1 triangle are congruent to two angles of another triangle, the three angles are congruent
2. each angle of an equiangular triangle is 60
3. in a triangle, there is at most one right or obtuse angle
4. the acute angles of a right triangle are complementary

Question 23

exterior angles theorem

Answer 23

the measure of the exterior angle of a triangle is the sum of the measure of 2 of its remote interior angles

Question 24

acute, obtuse, right, and equiangular

Answer 24

a triangle with….
acute: 3 acute angles
obtuse: 1 obtuse angle
right: 1 right angle
equiangular: all (3) congruent angles

Question 25

scalene, isosceles, equilateral

Answer 25

a triangle with…
scalene: no congruent sides
isosceles: at least 2 congruent sides
equilateral: all (3) congruent sides

Question 26

polygon

Answer 26

a shape where…
1. each segment intersects with exactly 2 others at 1 endpoint
2. no 2 segments sharing 1 endpoint are collinear

Question 27

convex polygon

Answer 27

a polygon with no sides pointing into its interior

Question 28

diagonal

Answer 28

a segment joining two nonconsecutive vertices

Question 29

polygon interior sum theorem

Answer 29

the sum of a convex polygon’s interior angles w/ n sides is (n-2)180

Question 30

polygon exterior sum theorem

Answer 30

the sum of the measures of a convex polygon’s exterior angles w/ n sides is 360

Question 31

concave polygons

Answer 31

when 1+ diagonal crosses outside the polygon

Question 32

irregular polygons

Answer 32

a polygon that is neither equiangular nor equilateral, much less regular