Unit 1: Postulates & Theorems

Question 1

Ruler Postulate

Answer 1

A shared understanding of how to use a ruler properly:
1. choose a consistent scale with equal increments
2. calculate the length (measure) by absolute distance

Question 2

Segment Addition Postulate

Answer 2

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

Question 3

Protractor Postulate

Answer 3

On line AB in a given plane, choose its midpoint (point O); all rays that can be drawn from O (ex: ray OA) are degrees
1. ray OA is 0 degrees, OB is 180
2. always measure the absolute value

Question 4

Angle Addition Postulate

Answer 4

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

Question 5

Line-Point Postulate

Answer 5

A line is defined by 2 or more points

Question 6

Plane-Point Postulate

Answer 6

A plane has 3 or more points not all in 1 line

Question 7

Space-Point Postulate

Answer 7

Space has 4 or more points not all in 1 plane of existence

Question 8

Two-Point Postulate

Answer 8

Through any 2 points, there is exactly 1 line

Question 9

Three-Point Postulate

Answer 9

Through any 3 points, there is at least 1 plane; any 3 noncollinear points there is exactly 1 plane

Question 10

Plane-Line Postulate

Answer 10

If 2 points are on a plane, then the line containing said points is also on said plane

Question 11

Plane Intersection Postulate

Answer 11

If 2 planes intersect, their intersection is a line

Question 12

Line Intersection Theorem

Answer 12

If 2 lines intersect, then they intersect at exactly 1 point

Question 13

Theorem: A Line and a Point Define a Plane

Answer 13

Through a line and a point not in the line, there is exactly 1 plane

Question 14

Theorem: Two Lines Define a Plane

Answer 14

If 2 lines intersect, there is exactly 1 plane that contains the lines