postulates and theroms and stuff

Question 1

Postulates 1 (ruler postulate)

Answer 1

points in a line can be matched 1:1 with real numbers. The real number that corresponds to a the coordinate of the point

Question 2

Postulate 2 (Segment Addition Postulate)

Answer 2

If B is between A & C, then AB + BC=AC

Question 3

Postulate 4 (Angle Addition Postulate)

Answer 3

If point B lies in the interior of <AOC, then m<AOB + m<BOC = m<AOC. If <AOC is a straight angle and B is any point not on line AC, then m<AOB + m<BOC=180

Question 4

Postulate 5

Answer 4

A line contains at least two points; a plane contains at least three points not all in one line; space contains at least 4 points not all in one plane

Question 5

Postulate 6

Answer 5

Through any 2 points there is exactly one line

Question 6

Postulate 7

Answer 6

Trough any three points there is at least one (infinite) plane, nd through any three noncollinear points there is exactly one plane (only one).

Question 7

Postulate 8

Answer 7

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

Question 8

Postulate 9

Answer 8

If 2 planes intersect, the their intersection is a line

Question 9

Theorem 1

Answer 9

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

Question 10

Theorem 2

Answer 10

Through a line and a point not in the line there is exactly 1 plane (similar to 3 noncollinear points)

Question 11

Theorem 3

Answer 11

If 2 lines intersect, then exactly 1 plane contains the lines

Question 12

Midpoint of a segment def

Answer 12

point equidistant from the endpoints of a line segment

Question 13

Bisector of a segment def

Answer 13

a figure that passes through the midpoint of a segment

Question 14

Midpoint Theorem

Answer 14

If M is the midpoint of line AB, then AM is ½AB and MB ½AB

Question 15

Angle Bisector Theorem

Answer 15

If BX if the bisector of <ABC, then m<ABC=½ m<ABC and m<XBC=½ m<ABC

Question 16

Vertical angles theorem

Answer 16

Vertical angles are congruent

Question 17

2 lines are perpendicular, then theorem

Answer 17

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

Question 18

converse of the perpendicular theorem

Answer 18

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

Question 19

If the exterior sides of two adjacent acute angles are perpendicular, then what theorem

Answer 19

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

Question 20

if two angles are supp of congruent angles, then

Answer 20

If two angles are supplements of congruent/ same angles, then the two angles are congruent

Question 21

if two angles are comp of congruent angles, then

Answer 21

if two angles are complements of congruent/ same angles, then the two angles are congruent

Question 22

Scalene

Answer 22

no sides are congruent

Question 23

Isosceles

Answer 23

at least 2 sides are congruent

Question 24

Equilateral

Answer 24

all sides are congruent

Question 25

Equiangular

Answer 25

all angles are congruent

Question 26

Polygon

Answer 26

many angles

Question 27

Convex polygon

Answer 27

a polygon which no line containing a side of the polygon contains a point in the interior of the polygon (simpler: not concave)

Question 28

Concave polygon

Answer 28

a polygon which caves in (you can draw a line connecting the points between it)

Question 29

Deductive reasoning

Answer 29

a conclusion based on accepted statements

Question 30

Inductive reasoning

Answer 30

a conclusion based on several past observations

Question 31

Corresponding Angles Converse Postulate

Answer 31

if 2 lines are cut by a transversal so that the corresponding angles are congruent, the lines are parallel

Question 32

If two parallel lines are cut by a third plane, theorem

Answer 32

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

Question 33

Alternate Interior Angles Converse Theorem

Answer 33

if 2 lines are cut buy a transversal so that the alternate interior angles are congruent, then the lines are parallel

Question 34

Same Side Interior Angles Converse Theorem

Answer 34

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

Question 35

Alternate Exterior Angles Converse Theorem

Answer 35

If 2 lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel

Question 36

If there is a line and a point not on the line, theorem

Answer 36

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line

Question 37

Two lines parallel to a third line are, theorem

Answer 37

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

Question 38

The sum of a triangle’s measures is what theorem

Answer 38

The sum of a triangle’s measures is 180

Question 39

The measure of an exterior angle of a triangle equals the sum of what theorem

Answer 39

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

Question 40

(n-2)180 theorem

Answer 40

The sum of the measure of the interior angles of a convex polygon with n sides is (n-2)180

Question 41

polygon exterior 360 theorem

Answer 41

The sum of the measures of the exterior angles of any convex polygon is 360 degrees.

Question 42

2 angles of one triangle are congruent to another 2 angles of a diff triangle, then what

Answer 42

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3 angles are congruent

Question 43

equilateral triangle measure is what

Answer 43

Each angle of an equilateral triangle has a measure of 60