103 terms

Note: this is a guide, it does not include everything, and it is advisable you review your notes

Collinear Points

points that lie on the same line

complementary angles

have a sum of 90 degrees

supplementary angles

have a sum of 180 degrees

exterior angle theorem

in a triangle; two interior angles equal the opposite exterior angle (x+y=z)

centroid

in a triangle; intersection of medians, (2x+x=3x)

orthocenter

in a triangle; intersection of altitudes

incenter

in a triangle; intersection of angle bisectors, center of inscribed circle

circumcenter

in a triangle; intersection of perpendicular bisectors, center of circumscribed circle

acute triangle

all angles less than 90 degrees, orthocenter, incenter, circumcenter, centroid all inside triangle

obtuse triangle

one angle greater than 90 degrees, orthocenter, circumcenter located outside, incenter, centroid located inside triangle

equilateral triangle

all angles equal (120 degrees) ortho-, in-, circumcenter, and centroid all inside and interest at same location

right triangle

one angle is 90 degrees, ortho- and circumcenter on triangle, incenter and centroid inside triangle

distance

square root of (X2-X1)^2+(Y2-Y1)^2

sum of interior angles

180(n-2)

sum of exterior angles

360 degrees

single interior angle

(180(n-2))/2

single exterior angle

360/n

equation of a line

y=mx+b OR Y-Y1=m(X-X1)

midpoint

(X1+X2)/2 AND (Y1+Y2)/2

slope

(Y1-Y2) / (X1-X2)

negative slope reciprocals

found in perpendicular lines

same slopes

found in parallel lines

equation of median

1) find midpoint 2) find slope from vertex to opposite midpoint 3) write equation using slope and midpoint

equation of altitude

1) fnd slope of opposite side 2) take negative reciprocal or slope 3) write eqaution using vertec and the negative reciprocal slope

equation of opposite bisector

1) find midpoint 2) find slope of opposite side and take negative reciprocal 3) write equation using negative reciprocal and midpoint

proving right triangle

how: using distance 3X and pythatgoreom theroem to show Pyth Thm works

proving isosceles triangle

how: distance 3X and Pythagorean theroem to show at least 2 sides are congruent and Pyth Thm works

proving parallelogram

how: distance 4X to show both pairs of opposite sides are congruent

proving rhombus

how: distance 4X to show all sides are congruent

proving rectangle

how: distance 6X to show both pairs of opposite sides are congruent and diagonals are congruent

proving square

how: distance 6X to show all sides are congruent and diagonals are congrent

proving trapzeoid

how: slope 4X to show only one pair of parallel lines

proving isosceles trapzeoid

how: slope 4X distance 2X to show one pair of parallel sides and the nonparallel sides are congruent

logic: p=true, q=true

~p=F, ~q=F, pVq=T, p^q=T, if p then q = T, if p and if q = T

logic: p=true, q=false

~p=F, ~q=T, pVq=T, p^q=F, if p then q = F, if p and if q = F

logic: p=false, q=true

~p=T, ~q=F, pVq=T, p^q=F, if p then q = T, if p and if q = F

logic: p=false, q=false

~p=T, ~q=T, pVq=F, p^q=F, if p then q = T, if p and if q = T

converse

reverse order of statement

inverse

negate both parts of statement

contrapositive

con- and inverse

CSSTP

corresponding parts of similar triangles are in proportion

Midsegment

connects two midpoints of a triangle; is 1/2 the size of parallel side

30' 60' 90'

side opposite right angle is 2n, opposite 60 is n-radical-3, opposite 30 is n; seen in equilateral triangles and rhombi

45' 45' 90'

side opposite 45 is n, opposite right angle is n-radical-2; seen in isosceles right triangle and squares

When Leg as Mean Proportional . .

whole hypotnuse / leg = leg / part hyp- (n/x=x/n-b)

When Altitude as Mean Propotional . .

part hypotnuse / altitude = altitude / part hyp- (a/x=x/b)

AA congruent to AA

two triangles are SIMILAR by two congruent angles

circle

locus of a point

perpendicular bisector

locus of 2 points

1 parallel line equidistant from given lines

locus of 2 parallel lines

2 parallel lines equidistant from given line

locus of 1 line

2 perpendicular angle bisectors

locus of two intersecting lines

positve rotations are always . .

counterclockwise

reflection of X-axis

(x,y) = (x,-y)

reflection of Y-axis

(x,y) = (-x,y)

reflection of y=x

(x,y) = (y,x)

reflection of y=-x

(x,y) = (-y,-x)

reflection of origin

(x,y) = (-x,-y)

Rotation of 90' OR -270'

(x,y) = (-y,x)

Rotation of 180' OR -180'

(x,y) = (-x,-y)

Rotation of 270' OR -90'

(x,y) = (y,-x)

orientation

order of vertices

isometry

preserves distance

opposite isometry

changes orientation (reflection)

direct isometry

preserves orientation

point symmetry

turn upside down and remains the same

central angle

equals intercepted arc (angle located on center)

right angle in a CIRCLE is formed by a_______

tangent and radius

inscribed angle

equals half the intercepted arc

angle formed by ________in a CIRCLE equals 180 - minus supplementary angle

secant and chord

angle outside circle is . .

half the difference of the larger arc and smaller arc (both intercepted)

angle inside circle is . .

half the sum of the two intercepted arc (angle not on center)

to find measurement with two secants . .

part of secant 1 times whole secant 1 equals part of secant 2 times whole secant 2 {(x(x+n)) = (y(y+m))}

to find measurement with secant and tangent . .

tangent squared equals part secant times whole secant (t^2) = p(s)

measurements of tangents are . .

congruent if from same point

when the diameter is perpendicular to the chord . .

the chord is bisected by diamter

to find measurement of two chords . .

partchord1 times part chord1 = partchord2 times partchord2

tetrahedron

4 faces, 4 vertices

octahedron

8 faces, 6 vertices

icosahedron

20 faces, 12 vertices

hexahedron

6 faces, 8 vertices (cube)

dodecahedron

12 faces, 20 vertices

area of square

side-squared (s^2)

area of triangle

base times hight divided by 2 (bh/2)

area of circle

pi-r-squared (er^2)

area of rectangle

length times width or base times hight (lw or bh)

volume of prism AND cylinder

area times hight (BH) B is the area of the base

lateral area (LA) of prism

ph (perimeter of the base times the hight of the prism)

surface area (SA) of prism

LA+2B (B is the area of the two bases, LA is the area of the faces)

lateral area of pyramid

half of perimeter times the slant hight (1/2 pl, with l being the slant hight)

surface area of pyramid

LA+B (lateral area of the faces time the area of the base)

quadrilateral

four sides polygon, has diagonals,

parallelogram

opposite sides congruent and parallel, opposite angle congruent, consecutive angles are supplementary, diagonals bisect

rectangle

defined by four right angles and congruent diagonals

rhombus

defined by all sides congruent, perpendicular diagonals, diagonals bisect angles, all angles are NOT congruent

square

defined as a rectangle and rhombus

trapezoid

exactly one pair of parallel sides

isosceles trapezoid

congruent legs and diagonals, one pair of parallel sides

Proofs

used with a statement and supported by a reason

tangent

intersects circle at one point

secant

intersects circle at two points

chord

connects two points of a circle

diameter

is a chord thats runs through center of circle