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Angles opposite one another when two lines intersect.
divides an angle into two congruent angles
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
A plane figure with the same size and shape.
Angles that add to 180 degrees.
Two angles whose sum is 90 degrees.
Degrees in a line
if a triangle has sides A, B, & C, and A <_ B <_ C <_, then
a regular polygon has all_______ congruent and all ________ congruent
Degrees in a circle
in a right triangle, the side opposite the right angle
two sides have the same length
two lines that intersect and form a right angle are
lines in the plane that are the same distance apart
the property of symmetry: if A=B then
the reflexive property: A=
the transitive property: if A=B and B=C, then A=
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).
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.
The collection of all points forms a nonempty set. There is more than one point in the set.
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
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
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.