Chapter 6/7 Theorems

Front 1

Postulate 10

Back 1

Three noncollinear points determine a plane.

Hint 1

https://o.quizlet.com/s3HStS89JAcUnU9mwqU6fg_m.jpg

Front 2

Theorem 45

Back 2

A line and a point not on the line determine a plane

Front 3

Theorem 46

Back 3

Two intersecting lines determine a plane.

Front 4

Theorem 47

Back 4

Two parallel lines determine a plane.

Front 5

Postulate 11

Back 5

If two planes intersect, their intersection is exactly one line.

Front 6

Definition of line and plane perpendicularity

Back 6

A line is perpendicular to a plane if it is perpendicular to every one of the lines in the plane that pass through its foot.

Front 7

Theorem 48

Back 7

If a line is perpendicular to two distinct lines that lie in a plane and that pass through its foot, then it is perpendicular to the plane.

Hint 7

https://o.quizlet.com/oqbXjyQfPhybY-LhCYj7Ww_m.jpg

Front 8

Definition of parallel lines 1

Back 8

A line and a plane are parallel if they do not intersect.

Hint 8

https://o.quizlet.com/Z9GDrsyI4oYttGlEqQ6IBA_m.jpg

Front 9

Definition of parallel lines 2

Back 9

Two planes are parallel if they do not intersect.

Hint 9

https://o.quizlet.com/LJyyjEag1jE38m-8723H1g_m.png

Front 10

Definition of parallel lines 3

Back 10

Two lines are skew if they are not coplanar.

Hint 10

https://o.quizlet.com/ioayheAU9vRR8pRWHD9ceA_m.jpg

Front 11

Theorem 49

Back 11

If a plane intersects two parallel planes, the lines of intersection are parallel.

Front 12

Parallelism of Lines and planes 1

Back 12

If two planes are perpendicular to the same line, they are parallel to each other.

Front 13

Parallelism of Lines and planes 2

Back 13

If a line is perpendicular to one of the two parallel plane, it is perpendicular to the other plane as well.

Front 14

Parallelism of Lines and planes 3

Back 14

If two planes are parallel to the same plane, they are parallel to each other.

Front 15

Parallelism of Lines and planes 4

Back 15

If two lines are perpendicular to the same plane, they are parallel to each other.

Front 16

Parallelism of Lines and planes 5

Back 16

If a plane is perpendicular to one of two parallel lines, it is perpendicular to the other line as well.

Front 17

Theorem 50

Back 17

The sum of the measures of the three angles of a triangle is 180°.

Front 18

Definition of triangle application

Back 18

An exterior angle of a polygon is an angle that is adjacent to and supplementary to an interior angle of the polygon.

Front 19

Theorem 51

Back 19

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

Front 20

Theorem 52(Midline theorem)

Back 20

A segment joining the midpoints of two midpoints of a triangle is parallel to the third side, and its length is one-half the length of the third side.

Front 21

Theorem 53(No-choice Theorem)

Back 21

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent.

Front 22

Theorem 54(AAS)

Back 22

If there exists a correspondence between the vertices of two triangles such that two angles and a non included side of one are congruent to the corresponding parts of the other, then the triangles are congruent.

Front 23

Triangle

Back 23

Polygon with 3 sides

Hint 23

https://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q_m.png

Front 24

Quadrilateral

Back 24

Polygon with 4 sides

Hint 24

https://o.quizlet.com/PhRTJH.MtlGqIDeopsop4A_m.png

Front 25

Pentagon

Back 25

5 sided polygon

Hint 25

https://farm4.staticflickr.com/3484/3733687366_5ed0a9bdca_m.jpg

Front 26

Hexagon

Back 26

6 sided polygon

Hint 26

https://o.quizlet.com/i/_XWCPLW7F3A1q1LZy2FkWw_m.jpg

Front 27

Heptagon

Back 27

7 sided polygon

Hint 27

https://o.quizlet.com/t.m63NccKfbQSDK2ap3UaQ_m.png

Front 28

Octagon

Back 28

8 sided polygon

Hint 28

https://o.quizlet.com/xMQJTp.rKkkati3nEV3S8g_m.jpg

Front 29

nonagon

Back 29

9 sided polygon

Hint 29

https://o.quizlet.com/R8ZAI2THgcr3GoT5qxePWw_m.png

Front 30

decagon

Back 30

10 sided polygon

Hint 30

https://o.quizlet.com/VOtjPWMIY2E1zVwZrYXFQw_m.jpg

Front 31

dodecagon

Back 31

12 sided polygon

Hint 31

https://o.quizlet.com/EeAvmqYqJjgMfRmPmZkIYA_m.png

Front 32

pentadecagon

Back 32

15 sided polygon

Hint 32

https://o.quizlet.com/L0SNpoa4.LXRMW-qf0.mrQ_m.png

Front 33

Theorem 55

Back 33

The sum S₁ of the measures of the angles of a polygon with n sides is given by the formula

Front 34

S₁=(n-2)180

Back 34

https://o.quizlet.com/i/w6wowdRLtZHrlnuTp77Z0g_m.jpg

Front 35

Finding interior angle of an angle polygon

Back 35

S₁=(n-2)180

Hint 35

https://o.quizlet.com/i/ka7G83GZPGR6ghribV1S1A_m.jpg

Front 36

Theorem 56

Back 36

If one exterior angle is taken at each vertex, the sum Sₑ of the measures of the exterior angles of a polygon is given by the formula Sₑ=360

Front 37

Sum of exterior angles formula

Back 37

Sₑ=360

Hint 37

https://o.quizlet.com/mjJRPaK-xp1J0ciSgBqrag_m.jpg

Front 38

Theorem 57

Back 38

The number of d diagonals that can be drawn in a polygon of n sides is given by the formula

Front 39

d=n(n-3)/2

Front 40

number of diagonals formula

Back 40

d= (n^2-3n)/2 or n(n-3)/2

Hint 40

https://o.quizlet.com/neU3k1oMS4m-3adtlI7ljQ_m.png

Front 41

Regular polygon

Back 41

A polygon that is both equilateral and equiangular.

Hint 41

https://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw_m.jpg

Front 42

Theorem 58

Back 42

The measure E of each exterior angle of an equiangular polygon of n sides is given by the formula

Front 43

E=360/n

Back 43

https://o.quizlet.com/LrqQvNA3vMjlc7mDeO0J5Q_m.png

Front 44

Finding exterior angle formula

Back 44

E=360/n

Hint 44

https://o.quizlet.com/mhlUSO93tKXkwf7LTMuVUg_m.jpg