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79 terms

Math rules for geometry

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Addition property
if a=b then a+c=b+c
Subtraction property
if a=b then a-b=b-c
Multiplication property
if a=b then a•c=b•c
Division property
if a=b then a/b=b/c
reflexive property
a=a
symmetric property
if a=b then b=a
transitive property
if a=b and b=c then a=c
substitution property
if a=b then b can replace a in any expression
distributive property
a(b+c)= ab+ac
vertical angles
two angles whose sides form two pair of opposite rays
adjacent angles
two coplanar angles with a common side, a common vertex, and NO common interior points
complementary angles
two angles whose measures have a sum of 90
supplementary
two angles whose measures have a sum of 180
Vertical angle theorem
vertical angles are congruent
Congruent supplements theorem
if two angles are supplements of the same angle (or of congruent angles) then the two angles are congruent
Congruent complements theorem
if two angles are complements of the same angle (or of congruent angles) then the two angles are congruent
right angles are congruent
if two angles are congruent and supplementary then each is a right angle
congruent angles
angles that have the same measure
2 points postulate
through any two points there is exactly one line
2 lines postulate
if two lines intersect then they intersect in exactly one point
2 planes postulate
if two planes intersect they intersect in exactly one line
3 points postulate
through any 3 noncollinear points there is exactly one plane
segment addition postulate
if three points A, B, C are collinear and B is between A and C the AB+BC=AC
Angle Addition Postulate
if B is in the interior of <AOC then m<AOB+m<BOC=<AOC
if <AOC is a straight angle then <AOB+<BOC=180
acute angle
less than 90
right angle
90
obtuse angle
more than 90
straight angle
180
perpendicular lines
2 lines that intersect to form right angles
angle bisector
a ray that divides an angle into two congruent coplanar angles
Distance formula
√(x₂-x₁)²+(y₂-y₁)²
Midpoint Formula
M= x₁+x₂/2, y₁+y₂/2
transversal
a line that intersects to coplanar lines
alternate interior angle
nonadjacent interior angles that lie on opposite sides of the transversal
same side interior angles
lie on the same side of the transversal
corresponding angles
lie on the same side of the transversal in corresponding positions
Corresponding angles postulate
if a transversal intersects two parallel lines then corresponding angles are congruent
alternate interior angles theorem
if a transversal intersects two parallel lines then alternate interior angles are congruent
same side interior theorem
if a transversal intersects two parallel lines, then same side interior angles are supplementary
converse of the corresponding angles postulate
if two line and a transversal form corresponding angles that are congruent, then the two lines are parallel
converse of the alternate interior angles theorem
if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel
converse of the same side interior angles theorem
if two line and a transversal form same side interior angles that are supplementary then the two lines are parallel
parallel lines theorem
if two lines are parallel to the same line then they are parallel to each other
perpendicular lines theorem
in a plane if two lines are perpendicular to the same line then they are parallel to each other
Triangle angle sum theorem
the sum of the measures of the angles of a triangle is 180
Triangle exterior angle theorem
the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
exterior angles of a polygon
angle formed by a side and an extension of an adjacent side
remote interior angles
the 2 angles not near the exterior angle
polygon
closed plane figure with at least three sides that are segments
convex polygon
has no diagonal with points outside the polygon
concave polygon
has at least one diagonal with points outside the polygon
polygon angle sum theorem
the sum of the measures of the angles of an n-gon is (n-2)180
polygon exterior angle sum theorem
the sum of the measures of the exterior angles of a polygon one at each vertex is 360
equilateral polygon
all sides are equal
equiangular polygon
all angles are equal
regular polygon
both angles and sides are equal
slope intercept form
y=mx+b
standard form
Ax+By=C
point-slope form
y-y₁=m(x-x₁)
to find slope
y₂-y₁
______

x₂-x₁
vertical line
x=
horizontal line
y=
to find y intercept
x=0
to find x intercept
y=0
Quadrilateral
4 sides
Pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagon
9 sides
decagon
10 sides
undecagon
11 sides
dodecagon
12 sides
acute triangle
all of its angles are acute
obtuse triangle
has one obtuse angle
scalene triangle
no sides or angles congruent
right triangle
has a right angle
isosceles
at least 2 congruent angles
slope of parallel lines
if two non vertical lines are parallel their slopes are equal.
slopes of perpendicular lines
if two non vertical lines are perpendicular the product of their slopes is -1