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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

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

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

______

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