question

Collinear Points

answer

points that lie on the same line

question

complementary angles

answer

have a sum of 90 degrees

question

supplementary angles

answer

have a sum of 180 degrees

question

exterior angle theorem

answer

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

question

centroid

answer

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

question

orthocenter

answer

in a triangle; intersection of altitudes

question

incenter

answer

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

question

circumcenter

answer

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

question

acute triangle

answer

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

question

obtuse triangle

answer

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

question

equilateral triangle

answer

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

question

right triangle

answer

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

question

distance

answer

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

question

sum of interior angles

answer

180(n-2)

question

sum of exterior angles

answer

360 degrees

question

single interior angle

answer

(180(n-2))/2

question

single exterior angle

answer

360/n

question

equation of a line

answer

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

question

midpoint

answer

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

question

slope

answer

(Y1-Y2) / (X1-X2)

question

negative slope reciprocals

answer

found in perpendicular lines

question

same slopes

answer

found in parallel lines

question

equation of median

answer

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

question

equation of altitude

answer

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

question

equation of opposite bisector

answer

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

question

proving right triangle

answer

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

question

proving isosceles triangle

answer

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

question

proving parallelogram

answer

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

question

proving rhombus

answer

how: distance 4X to show all sides are congruent

question

proving rectangle

answer

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

question

proving square

answer

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

question

proving trapzeoid

answer

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

question

proving isosceles trapzeoid

answer

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

question

logic: p=true, q=true

answer

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

question

logic: p=true, q=false

answer

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

question

logic: p=false, q=true

answer

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

question

logic: p=false, q=false

answer

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

question

converse

answer

reverse order of statement

question

inverse

answer

negate both parts of statement

question

contrapositive

answer

con- and inverse

question

CSSTP

answer

corresponding parts of similar triangles are in proportion

question

Midsegment

answer

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

question

30' 60' 90'

answer

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

question

45' 45' 90'

answer

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

question

When Leg as Mean Proportional . .

answer

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

question

When Altitude as Mean Propotional . .

answer

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

question

AA congruent to AA

answer

two triangles are SIMILAR by two congruent angles

question

circle

answer

locus of a point

question

perpendicular bisector

answer

locus of 2 points

question

1 parallel line equidistant from given lines

answer

locus of 2 parallel lines

question

2 parallel lines equidistant from given line

answer

locus of 1 line

question

2 perpendicular angle bisectors

answer

locus of two intersecting lines

question

positve rotations are always . .

answer

counterclockwise

question

reflection of X-axis

answer

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

question

reflection of Y-axis

answer

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

question

reflection of y=x

answer

(x,y) = (y,x)

question

reflection of y=-x

answer

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

question

reflection of origin

answer

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

question

Rotation of 90' OR -270'

answer

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

question

Rotation of 180' OR -180'

answer

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

question

Rotation of 270' OR -90'

answer

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

question

orientation

answer

order of vertices

question

isometry

answer

preserves distance

question

opposite isometry

answer

changes orientation (reflection)

question

direct isometry

answer

preserves orientation

question

point symmetry

answer

turn upside down and remains the same

question

central angle

answer

equals intercepted arc (angle located on center)

question

right angle in a CIRCLE is formed by a_______

answer

tangent and radius

question

inscribed angle

answer

equals half the intercepted arc

question

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

answer

secant and chord

question

angle outside circle is . .

answer

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

question

angle inside circle is . .

answer

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

question

to find measurement with two secants . .

answer

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

question

to find measurement with secant and tangent . .

answer

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

question

measurements of tangents are . .

answer

congruent if from same point

question

when the diameter is perpendicular to the chord . .

answer

the chord is bisected by diamter

question

to find measurement of two chords . .

answer

partchord1 times part chord1 = partchord2 times partchord2

question

tetrahedron

answer

4 faces, 4 vertices

question

octahedron

answer

8 faces, 6 vertices

question

icosahedron

answer

20 faces, 12 vertices

question

hexahedron

answer

6 faces, 8 vertices (cube)

question

dodecahedron

answer

12 faces, 20 vertices

question

area of square

answer

side-squared (s^2)

question

area of triangle

answer

base times hight divided by 2 (bh/2)

question

area of circle

answer

pi-r-squared (er^2)

question

area of rectangle

answer

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

question

volume of prism AND cylinder

answer

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

question

lateral area (LA) of prism

answer

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

question

surface area (SA) of prism

answer

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

question

lateral area of pyramid

answer

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

question

surface area of pyramid

answer

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

question

quadrilateral

answer

four sides polygon, has diagonals,

question

parallelogram

answer

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

question

rectangle

answer

defined by four right angles and congruent diagonals

question

rhombus

answer

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

question

square

answer

defined as a rectangle and rhombus

question

trapezoid

answer

exactly one pair of parallel sides

question

isosceles trapezoid

answer

congruent legs and diagonals, one pair of parallel sides

question

Proofs

answer

used with a statement and supported by a reason

question

tangent

answer

intersects circle at one point

question

secant

answer

intersects circle at two points

question

chord

answer

connects two points of a circle

question

diameter

answer

is a chord thats runs through center of circle

Geometry Regents Review

Unlock all answers in this set

Haven't found what you were looking for?

Search for samples, answers to your questions and flashcards