# Geometry Regents Review

question

Collinear Points

points that lie on the same line
question

complementary angles

have a sum of 90 degrees
question

supplementary angles

have a sum of 180 degrees
question

exterior angle theorem

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

centroid

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

orthocenter

in a triangle; intersection of altitudes
question

incenter

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

circumcenter

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

acute triangle

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

obtuse triangle

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

equilateral triangle

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

right triangle

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

distance

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

sum of interior angles

180(n-2)
question

sum of exterior angles

360 degrees
question

single interior angle

(180(n-2))/2
question

single exterior angle

360/n
question

equation of a line

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

midpoint

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

slope

(Y1-Y2) / (X1-X2)
question

negative slope reciprocals

found in perpendicular lines
question

same slopes

found in parallel lines
question

equation of median

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

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
question

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
question

proving right triangle

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

proving isosceles triangle

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

proving parallelogram

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

proving rhombus

how: distance 4X to show all sides are congruent
question

proving rectangle

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

proving square

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

proving trapzeoid

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

proving isosceles trapzeoid

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

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
question

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
question

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
question

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
question

converse

reverse order of statement
question

inverse

negate both parts of statement
question

contrapositive

con- and inverse
question

CSSTP

corresponding parts of similar triangles are in proportion
question

Midsegment

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

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
question

45′ 45′ 90′

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 . .

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

When Altitude as Mean Propotional . .

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

AA congruent to AA

two triangles are SIMILAR by two congruent angles
question

circle

locus of a point
question

perpendicular bisector

locus of 2 points
question

1 parallel line equidistant from given lines

locus of 2 parallel lines
question

2 parallel lines equidistant from given line

locus of 1 line
question

2 perpendicular angle bisectors

locus of two intersecting lines
question

positve rotations are always . .

counterclockwise
question

reflection of X-axis

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

reflection of Y-axis

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

reflection of y=x

(x,y) = (y,x)
question

reflection of y=-x

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

reflection of origin

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

Rotation of 90′ OR -270′

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

Rotation of 180′ OR -180′

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

Rotation of 270′ OR -90′

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

orientation

order of vertices
question

isometry

preserves distance
question

opposite isometry

changes orientation (reflection)
question

direct isometry

preserves orientation
question

point symmetry

turn upside down and remains the same
question

central angle

equals intercepted arc (angle located on center)
question

right angle in a CIRCLE is formed by a_______

question

inscribed angle

equals half the intercepted arc
question

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

secant and chord
question

angle outside circle is . .

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

angle inside circle is . .

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

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))}
question

to find measurement with secant and tangent . .

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

measurements of tangents are . .

congruent if from same point
question

when the diameter is perpendicular to the chord . .

the chord is bisected by diamter
question

to find measurement of two chords . .

partchord1 times part chord1 = partchord2 times partchord2
question

tetrahedron

4 faces, 4 vertices
question

octahedron

8 faces, 6 vertices
question

icosahedron

20 faces, 12 vertices
question

hexahedron

6 faces, 8 vertices (cube)
question

dodecahedron

12 faces, 20 vertices
question

area of square

side-squared (s^2)
question

area of triangle

base times hight divided by 2 (bh/2)
question

area of circle

pi-r-squared (er^2)
question

area of rectangle

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

volume of prism AND cylinder

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

lateral area (LA) of prism

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

surface area (SA) of prism

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

lateral area of pyramid

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

surface area of pyramid

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

four sides polygon, has diagonals,
question

parallelogram

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

rectangle

defined by four right angles and congruent diagonals
question

rhombus

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

square

defined as a rectangle and rhombus
question

trapezoid

exactly one pair of parallel sides
question

isosceles trapezoid

congruent legs and diagonals, one pair of parallel sides
question

Proofs

used with a statement and supported by a reason
question

tangent

intersects circle at one point
question

secant

intersects circle at two points
question

chord