# Geometry Postulates, Theorems,Definition, and Corrlaries

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1. P1 Ruler Postulate
the distance between any two points equals the absolute value of the difference of their coordinates
If B is between A and C, then AB+BC=AC
3. P3 Protractor Postulate
with any given angle, a line/ray/segment can be drawn (use for drawing auxillary line)
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 ant not on lineAC, then m∠AOB+m∠BOC=180
5. P5 A line contains at least ____; a plane contains at least ____ not____; space contains at least ____ not ____
two points; three points not all in one line; four points not all in one plane
6. P6 Through two points...
there is exactly one line
7. P7 Through any three points ____; through any three ____ points
8. T4-5 If a point lies on the perpendicular bisector of a segment then
the point is equidistant from the segments' endpoint
9. 14-6 If a point is equidistant from the endpoints of the segment then
the point lies on the perpendicualar bisector of the segment
10. 14-7 If a point lies on the bi. of an angle then
the point is equidistant from the sides of the angle
11. T4-8 If a point is equidistant from the sides of an angle then
the point lies on the angle's bisector
12. Def of ▱
quad. w/ both oppostie sides parallel
13. T5-1 If ▱ then both pairs of ____ sides are ____
opp.; congruent
14. T5-2 If ▱ then both pairs of opp. a_____ are _____
angles; congruent
15. T5-3 If ▱ then d______ ______ each other
diag. bisects
16. T5-8 If two lines are parrallel, then all ______ on one _____ are _______ from the other _________
points; line; equidistant; line
17. T5-9 If 3 parallel lines cut off _________ segments one one transversal, then they cut off congruent on every _________
congruent; transversal
18. T5-10 A line that contains the midpoint of one side of a traingle and is parallel to another side passes through the _______ of the ________ __________
midpoint; third side
19. T5-11 The segment that joins the midpoints of two sides of a triangle (1)? and (2)?
• (1) is parallel to the third side
• (2) is half as long as the third side