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20 Cards in this Set

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Euclid's First Postulate

If A and B are points there is a unique line between them.

Euclid's Second Postulate

If AB and CD are line segments, there is a unique point E so that B is between A and E and BE=CD

Euclid's Third Postulate

For Distinct points O and A there is a circle with center O and radius OA.

Euclid's Fourth Postulate

All right angles are congruent

Euclid's Fifth Postulate

Parallel Postulate: Given a line l and a point P not on l, there is a unique line m that is parallel to l and goes through P

I1

For every point P and every point Q (not equal to P) there is a unique line l incident with P and Q

I2

For every line l there are at least two distinct points incident with l

I3

There exists three distinct points with the property that no line is incident with all three points

B1

if A*B*C the A*B*C are all distinct points on the same line and C*B*A

B2

if B doesn't equal D then there are A,C,D so A*B*D, B*C*D, and B*D*E (tells us there are infinitely many points. Many models fail this)

B3

If A,B,C all lie on a line, exactly one A*B*C, B*C*A, C*A*B is true

B4

For every line l and points A,B,C not on l: a) if A,B are on the same side of l and B,C are on the same side then A,C are on the same side. b) if A,B are on opposite sides and B,C are on opposite sides then A,C are on the same side of l

C1

If A not equal to B are distinct points and A' is a point and r is a ray from A', then there is a unique point B' on that ray so that A'B' congruent AB

C2

if AB congruent CD and AB congruent EF, then CD congruent CF. Also Ab congruent AB

C3

A*B*C & A'*B'*C' and AB congruent A'B' and BC congruent B'C', then AC congruent A'C'

C4

Given any angle ABC and another ray A'C' there is a unique ray B'C' on either side of A'B' such that angle ABC is congruent to angle A'B'C' (we can move angles)

C5

If angle A congruent angle B and angle A congruent angle C then angle B congruent angle C. Also angle A congruent angle A

C6

SAS

AIAT

If two lines are cut by a transversal and have a congruent pair of alternate interior angles, then the lines are parallel

EAT

An exterior angle to a triangle is larger than either of its remote interior angles