chapter 3

Question 1

parallel lines

Answer 1

coplanar lines that do not intersect

Question 2

skew lines

Answer 2

non coplanar lines (neither parallel nor intersecting)

Question 3

theorem about parallel planes

Answer 3

If two parallel planes are cut by a third plane, then the lines of intersection are parallel

Question 4

transversal

Answer 4

a line that intersect two or more coplanar lines in different points

Question 5

interior angles

Answer 5

inside the two lines cut by the transversal

Question 6

exteriors angles

Answer 6

outside the two lines cut by the transversal

Question 7

corresponding angles postulate

Answer 7

If 2 parallel lines are cut by a transversal, then corresponding angles are congruent

Converse:
If 2 lines are cut by a transversal and corresponding angles are congruent, then the two lines are parallel

Question 8

postulate about alternate interior angles

Answer 8

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

converse:
If 2 lines are cut by a transversal and alternate interior angles are congruent, then the two lines are parallel

Question 9

theorem about same side interior angles

Answer 9

If 2 parallel lines are cut by a transversal, then same-side interior angles are supplementary

converse:
If 2 lines are cut by a transversal and same side interior angles are supplementary, then the two lines are parallel

Question 10

theorem about perpendicular lines

Answer 10

If a transversal is perpendicular to one of the parallel lines, then it is also perpendicular to the other one.

converse:
If 2 lines are perpendicular to the same line, then the two lines are parallel.

Question 11

theorems (3)

Answer 11

Through a point outside a line, there is exactly one line parallel to the given line.

Through a point outside a line, there is exactly one line perpendicular to the given line.

Two lines parallel to a third line are parallel to each other.

Question 12

classification of triangles by sides

Answer 12

equilateral: 3 congruent sides
isosceles: at least 2 congruent sides
scalene: no congruent sides

Question 13

classification of triangles by angles

Answer 13

acute: 3 acute angles
equiangular: 3 congruent angles (60 degrees)
right: 1 right angle
obtuse: 1 obtuse angle

Question 14

triangle angle-sum theorem

Answer 14

The sum of the three angles of a triangle is 180

Question 15

third angle theorem

Answer 15

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent

Question 16

angles of equilateral triangles

Answer 16

equilateral triangles are also equiangular, so each angle of an equilateral triangle is 60 degrees.

Question 17

exterior angle theorem

Answer 17

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Question 18

consecutive vertices

Answer 18

2 vertices that are endpoints on the same side

Question 19

diagonal

Answer 19

a segment that join 2 non consecutive vertices of a polygon

Question 20

convex polygons

Answer 20

vertices are outside the shape

Question 21

concave (nonconvex) polygons

Answer 21

at least 1 vertex on the inside

Question 22

regular polygon

Answer 22

equilateral and equiangular

Question 23

polygon angle sum formula

Answer 23

n = number of sides
(n-2) x 180

Question 24

for any polygon (flow)

Answer 24

sum of interior angles: (n-2) x180
sum of exterior angles: 360

Question 25

for regular polygons (flow)

Answer 25

n (number of sides) = 360/measure of exterior angle