Vocabular Words

Question 1

Space

Answer 1

Set of all points

Question 2

Collinear points

Answer 2

Points are collinear iff they are on the same line

Question 3

Coplanar points

Answer 3

Points are coplanar iff they are on the same plane

Question 4

Noncollinear points

Answer 4

Points are not collinear iff they are not on the same line

Question 5

Noncoplanar points

Answer 5

Points are not coplanar iff they are not on the same plane

Question 6

Postulates

Answer 6

A statement that is accepted to be true without proof

Question 7

(Def.) In Betweeness of Points

Answer 7

B is between A and C iff they are collinear + the distance from A to B plus the distance from B to C equals the distance from A to C.

Shorter Version: A-B-C iff they are collinear and AB + BC = AC

Question 8

(Def.) Midpoint

Answer 8

A point is a midpoint of a segment iff it divides the segment into 2 congruent segments or 2 equal lengths + collinear to the other points

Question 9

(Def.) Congruent Segments

Answer 9

Segments are congruent iff their lengths are equal

Question 10

(Def.) Acute angle

Answer 10

An angle is acute iff its measure is less that 90 degrees

Question 11

(Def.) Right angle

Answer 11

an angle is a right iff its measure is 90 degrees

Question 12

(Def.) Obtuse angle

Answer 12

An angle is obtuse iff its measure is greater than 90 degrees and less that 180 degrees

Question 13

(Def.) Straight angle

Answer 13

an angle is a straight angle iff its measure is 180 degrees

Question 14

(Def.) Adjacent

Answer 14

share a ray

Question 15

(Def.) Betweeness of Rays

Answer 15

Ray OA - Ray OB - Ray OC iff they are coplanar and the measure of (m <AOB) + measure of (m <BOC) = measure of (m <AOC)

Question 16

(Def.) Congruent angles

Answer 16

Angles are congruent iff the measures are equal

Question 17

(Def.) Midray

Answer 17

A ray is a midray of an angle iff it divides the angle into 2 congruent angles or into 2 equal measures

Question 18

(Def.) Complementary Angles

Answer 18

2 angles are complementary iff the sum of their measures is 90 degrees

Question 19

(Def.) Supplementary Angles

Answer 19

2 angles are supplementary iff the sum of their measures is 180 degrees

Question 20

(Def.) Perpendicular Lines

Answer 20

Lines are perpendicular iff they form right angles

Question 21

Postulate 5

Answer 21

• A line contains at least 2 points
• A plane contains at least 3 noncollinear points
• Space contains at least 4 noncoplanar points

Question 22

Postulate 6

Answer 22

• Through any 2 points there is exactly 1 line
• 2 points determine a line

Question 23

Postulate 7

Answer 23

• Through any 3 points, there is at least 1 plane
• Through any 3 noncollinear points there is exactly 1 plane
• 3 noncollinear points determine a plane

Question 24

Postulate 9

Answer 24

If 2 planes intersect, then their intersection is a line

Question 25

Postulate 8

Answer 25

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

Question 26

Theorem 1-1

Answer 26

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

Question 27

Theorem 1-2

Answer 27

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

Question 28

Theorem 1-3

Answer 28

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

Question 29

What is A.F.D?

Answer 29

Assume from drawing:
1) Betweeness of points
2) Betweenes of Rays
3) Straight angles
4) verticle angles
5) adjacent

Question 30

(Def.) In Betweeness of Points Theorems

Answer 30

1) If A-B-C, then they are collinear and AB + BC = AC
2) If AB + BC = AC, then A-B-C

Question 31

(Def.) Midpoint Theorems

Answer 31

1) If a point is a midpoint of a segment, then it divides the segment into 2 congruent segments or 2 equal lengths + collinear to the other points
2) If a point divides a segment into 2 congruent segments or 2 equal lengths, then it is a midpoint
3) If a point is a midpoint, then it divides a segment into 2 segments half as long

Question 32

(Def.) Verticle Angles

Answer 32

If 2 angles are verticles then they are congruent/have equal measures

Question 34

Congruent Segments Theorems

Answer 34

1) If segments are congruent, then their lengths are equal
2) If segments have equal lengths then they are congruent

Question 35

Acute angle Theorems

Answer 35

1) If an angle is acute, then its measure is less than 90 degrees
2) If the measure of an angle is less than 90 degrees, then it is an acute angle

Question 36

Right angle Theorems

Answer 36

1) If an angle is a right, then its measure is 90 degrees
2) If the measure of an angle is equal to 90 degrees, then it is a right angle

Question 37

Obtuse angle Theorems

Answer 37

1) If an angle is obtuse, then its measure is greater than 90 degrees and less than 180 degrees
2) If an angle’s measure is greater than 90 degrees and less than 180 degrees, then it is obtuse

Question 38

Straight angle Theorems

Answer 38

1) If an angle is a straight angle, then its measure is 180 degrees
2) If the measure of an angle is 180 degrees, then it is a straight angle

Question 39

Betweeness of Rays Theorems

Answer 39

1) If Ray OA - Ray OB - Ray OC, then they are coplanar, and the m <AOB) + m <BOC = m <AOC
2) If the m <AOB) + m <BOC = m <AOC, then Ray OA - Ray OB - Ray OC

Question 40

Congruent angles Theorems

Answer 40

1) If angles are congruent, then the measures are equal
2) If the measures of angles are equal, then they are congruent

Question 41

Midray Theorems

Answer 41

1) If a ray is a midray of an angle, then it divides the angle into 2 congruent angles or two angles with equal measures
2) If a ray divides an angle into 2 congruent angles or two angles with equal measures, then it is a midray
3) If a ray is a midray, then it divides an angle into two angles each half as large

Question 42

Complementary Angles Theorems

Answer 42

1) If 2 angles are complementary, then the sum of their measures is 90 degrees
2) If angles are complementary to the same angle, then they are congruent or have equal measures
3) If angles are the complement of congruent angles, then the angles are congruent

Question 43

Supplementary Angles Theorems

Answer 43

1) If 2 angles are supplementary, then the sum of their measures is 180 degrees
2) If angles are supplementary to the same angle, then they are congruent or have equal measures
3) If angles are the supplement of congruent angles, then the angles are congruent

Question 44

Vertical Angles Theorem

Answer 44

If 2 lines form a vertical angle, then they are congruent

Question 45

Linear Pair Theorem

Answer 45

If two angles form a linear pair, then they are supplements