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Vertical Angles

Angles opposite one another when two lines intersect.

a bisector

divides an angle into two congruent angles

a midpoint

divides a line into two congruent segments

a rectangle has

four right angles and two pairs of parallel lines

a parallelogram has

two pairs of parallel sides

a square has

four right angles, four congruent sides, and two pairs of parallel sides

a rhombus has

four congruent sides, and two pairs of parallel sides

a trapezoid has

one pair of parallel sides

corresponding angles are congruent

if two parallel lines are cut by a transversal then

Congruent

A plane figure with the same size and shape.

Supplementary

Angles that add to 180 degrees.

Complementary

Two angles whose sum is 90 degrees.

180°

Degrees in a line

A+B>C

if a triangle has sides A, B, & C, and A <_ B <_ C <_, then

sides, angles

a regular polygon has all_______ congruent and all ________ congruent

360°

Degrees in a circle

Hypotenuse

in a right triangle, the side opposite the right angle

Isosceles

two sides have the same length

perpendicular

two lines that intersect and form a right angle are

parallel

lines in the plane that are the same distance apart

B=A

the property of symmetry: if A=B then

a

the reflexive property: A=

c

the transitive property: if A=B and B=C, then A=

Length Postulate

To every segment we can assign a positive number called length that represents how many times a chosen unit length (meter, centimeter, inch, etc.) fits into the segment.

Measures Addition Postulate

We can add and subtract measures (lengths of segments).

Parts-whole Postulate

The whole is equal to the sum of its parts.

Angle Measurement Postulate

To every angle we can assign a non-negative number that represents how many times a chosen angle unit fits into the measured angle.

Parts-whole Postulate (angle addition)

The sum of the parts is equal to the whole.

Postulate about two lines and transversal

If two lines are intersected by a transversal so that the alternate interior (exterior) angles are congruent, then the lines are parallel.

Parallel Line Postulate

Through a point not on a given line, there is only one line parallel to the given line.

Postulate about two parallel lines and transversal

If two parallel lines are intersected by a transversal, then their alternate interior (exterior) angles are congruent.

Existence Axiom

The collection of all points forms a nonempty set. There is more than one point in the set.

Incidence Axiom

Every line is a set of points. For every pair of distinct points A and B there is exactly one line l such that A on l and B on l.

Ruler Placement Postulate

For every pair of distinct points P and Q, there is a coordinate function f: PQ -> R such that f(P)=0 and f(Q)>0.

Plane Separation Postulate

For every line l, the points that do not lie of l form two disjoint, nonempty sets H1 and H2, called half-planes bounded by l, such that

Protractor Postulate

Given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180.

Side Angle Side Postulate

If tri ABC and tri DEF are two triangles such that AB congruent to DE, <ABC congruent to <DEF, and BC congruent to EF, then tri ABC is congruent to tri DEF

Reflection Postulate

For every line l there exists a transformation rho.l: P->P, called the reflection in l such that

Euclidean Parallel Postulate

For every line l and for every external point P, there is exactly one line m such that P lies on m and m//l.

Elliptic Parallel Postulate

For every line l and for every external point P, there is no line m such that P lies on m and m//l.

Hyperbolic Parallel Postulate

For every line l and for every external point P, there are at least two lines m and n such that P lies on both m, n and m//l, n//l.