Geometry Regents Review

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

Get instant access to
all materials

Become a Member