Geometry #3 (Theorems, Postulates, Definitions)

Question 1

AM + MB = AB

AB - AM = MB
AB - MB = AM

Answer 1

1) Segment Addition Postulate
2) Segment Subtraction Postulate

Question 2

m<AOB + m<BOC = m<AOC

m<AOC - m<AOB = m<BOC
m<AOC - m<BOC = m<AOB

Answer 2

1) Angle Addition Postulate
2) Angle Subtraction Postulate

Question 3

a = b
b = c

a+b = b+c

Answer 3

Addition Property

Question 4

a = b
c = d

a-c = b-d

Answer 4

Subtraction Property

Question 5

a = b

ca = cb

Answer 5

Multiplication Property

Question 6

a = b

a/c = b/c

Answer 6

Division Property

Question 7

a = a

Answer 7

Reflexive Property

Question 8

a = b , b = a

Answer 8

Symmetric Property

Question 9

a = b
b = c

a = c

Answer 9

Transitive Property

Question 10

a = b
c = b

a = c

Answer 10

Substitution Property

Question 11

Def. of a Segment Bisector

Answer 11

A bisector of a segment is a line, segment, ray, or plane that intersects the segment at its midpoint.

Question 12

Def. of a Midpoint

Answer 12

A midpoint divides a segment into 2
congruent segments.

Question 13

Midpoint Theorem

Answer 13

A midpoint divides a segment in half.

Question 14

Def. of an Angle Bisector

Answer 14

A ray that divides an angle into two congruent adjacent angles.

Question 15

Angle Bisector Theorem

Answer 15

Forms two angles that are 1/2 the measure of the given angle.

Question 16

Adjacent Angles

Answer 16

Two angles that share a common vertex and common side, but no common interior.

Question 17

Def. of Complementary Angles

Answer 17

Two angles that sum of to 90* are complementary.

Question 18

Def. of a Linear Pair

Answer 18

If two adjacent angles form a straight line, then they are supplementary.
Two angles are a linear pair if and only if they have a common side and their other sides are opposite rays.

Question 19

Def. of Supplementary Angles

Answer 19

Two angles that sum up to 180*.

Question 20

Def. of Vertical Angles

Answer 20

The sides of one angle are opposite to the sides of the other angle.

Question 21

<1 is congruent to <2
(vertical angles)

Answer 21

Vertical angles are congruent.

Question 22

Line a is perpendicular to line b if and only if <1 is a right angle.

Answer 22

Perpendicular lines form right angles.

Question 23

<1 is congruent to <2
(right angles)

Answer 23

All right angles are congruent.

Question 24

If line AE is perpendicular to line FC, then <AFC is congruent to <EFC.

Answer 24

If two lines are perpendicular, then they form congruent adjacent angles.

Question 25

If <AFC is congruent to <EFC, then line AE is perpendicular to line FC.

Answer 25

If two lines form congruent adjacent angles, the lines are perpendicular.

Question 26

Memorize
(If the exterior of…)

Answer 26

If the exterior of two adjacent acute angles are perpendicular, then the angles are complementary.

Question 27

<1 is supp. to <2
<3 is supp. to <4
<2 is congruent to <3

<1 is congruent to <4

Answer 27

Supplements of congruent angles (or the same angle) are congruent.

Question 28

<6 is comp. to <7
<8 is comp. to <9
<7 is congruent to <8

<6 is congruent to <9

Answer 28

Complements of congruent angles (or the same angle) are congruent.

Question 29

Through any 2 points there is exactly __ line.

Answer 29

Through any 2 points there is exactly one line.

Question 30

A line contains at least __ points; a plane contains at least __ points not all in one line; space contains at least __ points not all in one plane.

Answer 30

A line contains at least 2 points; a plane contains at least 3 non-collinear points; space contains at least four non-coplanar points.

Question 31

Through any __ points there is at least one plane.
Through any __ non-collinear points, there is exactly one plane.

Answer 31

Through any 3 points there is at least one plane.
Through any 3 non-collinear points, there is exactly one plane.

Question 32

If __ points are in a plane, then the line that contains the points is in that plane.

Answer 32

If 2 points are in a plane, then the line that contains the points is in that plane.

Question 33

If two planes intersect, then their intersection is a __.

Answer 33

If two planes intersect, then their intersection is a line.

Question 34

If 2 lines intersect, then they intersect in exactly __ point.

Answer 34

If 2 lines intersect, then they intersect in exactly one point.

Question 35

Through a line and a point not in the line, there is exactly __ plane.

Answer 35

Through a line and a point not in the line, there is exactly one plane.

Question 36

If 2 lines intersect, then exactly __ plane contains the lines.

Answer 36

If 2 lines intersect, then exactly one plane contains the lines.