# Geometry Postulates and Theorems

### 27 terms by kenziemonroe

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### Postulate one

equal quantities plus equal quantities are equal

### postulate two

any given quantity equals itself

### postulate three

equal quantities minus equal quantities are equal

### theorem one

if one quantity equals a second and the second equals a third, then the first equals the third

### postulate four

construct line segement

construct circle

### theorem two

if a line segment is given, then another line segment can be constructed equal to it

sss

sas

### theorem three

if a line segment is given, then its midpoint can be determined

### theorem four

if an angle is given, the an angle can be constructed equal to it

### theorem five

if an angle is given, then its bisector can be constructed

### theorem seven

if a triangle has two sides equal, then the angles opposite these sides are equal

### theorem seven

if a point is not on a line segment, then a perpendicular from the point to the line segment can be constructed

### postulate nine

equal quantities multiplied or divided by equal quantities are equal

### postulate ten

with a straightedge, any given line segment can be extended

substitution

### theorem nine

if perpendicular then ninety degrees

### theorem ten

if ninety degrees then perpendicular

asa

### theorem eleven

if a transversal forms equal alt. interior angles with two line segments, then the line segments form parallels

### theorem eight

vertical angles are equal

### postulate eight

any whole quantity equals the sum of its parts

### postulate thirteen

there is exactly one parallel to a given line through a point that is not on the line

### theorem twelve

if two lines are parallel then the alt. interior angles are equal

### theorem thirteen

if a transversal form equal corresponding angles with two line segments, then the line segments are parallel

### theorem fourteen

if two lines are parallel then he corresponding angles are equal

Example: