103 terms

Geometry Regents Review

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