Jackie Kornstein
Final Math Review Sheet
Test 1
Undefined Terms:
Point
Line
Plane
Space
Definitions
Postulates - results that cannot be proven
Theorems - statements or results that can be proven
Lemma - tiny theorem that helps you prove another theorem
Corollaries - tiny theorem that follows easily from another theorem
Ray - If ray AB is a ray, then ray AB is a piece of a line with one endpoint.
Line Segment - If line CD is a line segment, then line CD is a part of a line with two
endpoints.
Angle - If angle XYZ is an angle, then it is made of two rays with a common
endpoint.
Degrees/Minutes/Seconds:
1 degree = 60 minutes
1 minute = 1/60 of a degree (60 = 1)
1 second = 1/60 of a minute (60 = 1)
Acute Angle - If an angle is an acute angle, then it measures less than 90.
Right Angle – If an angle is a right angle, then it measures 90
Obtuse Angle - If an angel is an obtuse angle, then it measures more than 90 but
less than 180.
Straight Angle - If an angle is a straight angle, then it measures 180.
Congruent - same size and same shape
Congruent Angles - If two angles are congruent, then they have equal measures.
Congruent Segments - If two segments are congruent, then they have equal
measures.
Intersection - overlapping part 
Union - add the two sets together (whole thing) 

Test 2
Definitions
Midpoint – If a point divides a segment into two congruent parts, then it is a
midpoint.
Bisector – If a point, line, or ray divides a segment into two congruent parts, it is the
bisector of the segment.
Trisectors – If two rays, lines, or segments divide an angle into three congruent
parts, then they are trisectors of the angle.
Perpendicular – If two lines intersect at right angles, then they are perpendicular.
Complementary – If two angles are complementary, then their measures add up to
90°.
Supplementary – If two angles are supplementary, then their angles add up to 180°.
Opposite Rays – If two rays go in opposite directions and have a common
endpoint, then they are opposite rays. (must form a line)
Vertical Angles – If two angles are vertical angles, then they are formed by two pairs
of opposite angles.
Theorems
 If two angles are right angles, then they are congruent.
 If two angles are straight angles, then they are congruent.
 If two angles are complementary or supplementary to the same angle, then
those two angles are congruent.
 If two angles are complementary or supplementary to congruent angles,
then those two angles are congruent.
 If the same segment is added to two congruent segments, then the sums are
congruent.
congruent + same = congruent
congruent – same = congruent
 If congruent segments are added to two congruent segments, then the sums
are congruent.
congruent + congruent = congruent
congruent – congruent = congruent
 Like Multiples – If segments or angles are congruent, their like multiples are
congruent.
 Like Divisions – If segments or angles are congruent, their like divisions are
congruent.
 Transitive Property – If two angles are congruent to the same angle, then
they are congruent.
 Double Transitive Property – If two angles are congruent to congruent
angles, then they are congruent to each other.
 Substitution Property – If angle 1 is complementary to angle 2 and angle 2 is

congruent to angle 3, then angle 1 is complementary to angle 3.
If two angles are vertical angles, then they are congruent.
Assumed
 straight lines
 straight angles
 collinear points (on the same line)
 one point is between another two points
 relative location of points
 vertical angles
Test 3
Types of Triangles
1. Scalene Triangle – If a triangle is a scalene triangle, then it is a triangle in which no
two sides are congruent.
2. Isosceles Triangle – If a triangle is an isosceles triangle, then it is a triangle in
which at least two sides are congruent.
3. Equilateral Triangle – If a triangle is an equilateral triangle, then it is a triangle in
which all sides are congruent.
4. Equiangular Triangle – If a triangle is an equiangular triangle, then it is a triangle
in which all angles are congruent.
5. Acute Triangle – If a triangle is an acute triangle, then it is a triangle in which all
angles are acute.
6. Right Triangle – If a triangle is a right triangle, then it is a triangle in which one of
the angles is a right angle. (The side opposite the right angle is called the
hypotenuse. These sides that form the right angle are called legs.)
7. Obtuse Triangle – If a triangle is an obtuse triangle, then it is a triangle in which
one of the angle is an obtuse angle.
Definitions
Circle – If there is a set of all points that are equidistant from a given point called
the center, then it is a circle.
Median – If a triangle has a line segment that goes from a vertex to the midpoint of
the opposite side, then it is the median of the triangle.
Altitude – If a triangle has a line that goes from a vertex and is perpendicular to the
opposite side, then it is the altitude of the triangle.
Angle Bisector – If a triangle has a line segment that goes from a vertex of a
triangle to the opposite side and bisects the angle of the triangle, then it is the
angle bisector of the triangle.
Exterior Angle – An exterior angle of a triangle is formed by one side of the triangle
and the extension of another side.
Equidistant – equal distances
Adjacent Angles – If a ray divides an angle into two different angles (not necessarily
congruent), then the two newly formed angles are adjacent angles. (Adjacent
angles can be assumed from the diagram.)
Theorems
 Congruent Triangles – If all three pairs of corresponding sides are congruent
and all three pairs of corresponding angles are congruent, then two triangles
are congruent.
(CPCTC – corresponding parts of congruent triangles are congruent)
 If it is a circle, then all radii are congruent.
 If a triangle is isosceles, then the base angles are congruent.
 If a two sides of a triangle are congruent, then the angles opposite them are
congruent.
 If two sides of a triangle are congruent, then the two base angels opposite
them are congruent.
 If a triangle is an equiangular triangle, then it is an equilateral triangle.
 If a triangle is an equilateral triangle, then it is an equiangular triangle.
 Hypotenuse-Leg (HL) – If two triangles are right triangles and the
hypotenuses are congruent and on pair of legs are congruent, then the
triangles are congruent.
 If two lines intersect to form congruent adjacent angles, then the lines are
perpendicular.
 If two angles are both supplementary and congruent, then they are right.
 In an isosceles triangle, the median to the base is also the altitude.
 In an isosceles triangle, the altitude to the base is also the median.
 In an isosceles triangle, the median to the base is also the angle bisector.
 In an isosceles triangle, the angle bisector to the base is also the median.
 In an isosceles triangle, the altitude to the base is also the angle bisector.
 In an isosceles triangle, the angle bisector to the base is also the altitude.
Postulates
 If all three pairs of corresponding sides are congruent, then the triangles are
congruent. (SSS)
 If two pairs of corresponding sides and the included angle are congruent,
then the triangles are congruent. (SAS)
 If two pairs of corresponding angles and the included side are congruent,
then the triangles are congruent. (ASA)
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Reflexive Postulate – Any angle or segment is congruent to itself.
Two points determine a line.
Test 4
Definitions
Distance Between Two Objects – length of a segment connecting the objects
(distance from a point to a line is measure along the perpendicular because that is
the shortest distance)
Perpendicular Bisector of Segment – a line/segment that bisects the segment and
makes a right angle
Plane – flat surface
Coplanar – on the same plane
Noncoplanar – no on the same plane
Transversal – a line that crosses two other lines
Interior Region – region between two lines
Exterior Region – region outside two lines
Alternate Interior Angles – pair of angles in the interior region on alternate side of
the transversal (Z)
Alternate Exterior Angles – pair of angles in the exterior region on alternate sides of
the transversal (V)
Corresponding Angles – two angles that are in corresponding positions (F)
Parallel Lines – two coplanar lines that never intersect
Skew Lines – two no coplanar lines that never intersect
Concurrent Lines – three or more lines that intersect at the same point (three
medians of a triangle are always concurrent)
Oblique Lines – two lines that intersect and are not perpendicular
Exterior Angle of a Triangle (or any polygon) – an angle that is adjacent and
supplementary to an interior angle of the triangle (or polygon)
Remote interior angle of a Triangle – angles that are not adjacent to the exterior
angles
Polygon – planar figure with three or more sides
closed
sides must be segments
sides only intersect at endpoints
only two sides intersect at each point
consecutive/adjacent sides are noncollinear
Diagonal of a Polygon – a segment connecting two non-adjacent vertices
Regular Polygon – A polygon that is both equilateral and equiangular.
Theorems
 ET#1 - If two points are each equidistant from the endpoints of a segment,
then the two points determine the perpendicular bisector of that segment.
 ET#2 – If a point is on the perpendicular bisector of a segment the it is
equidistant from the endpoints of that segment.
 The Lies-On Theorem (LIZON) – If a point is equidistant from the endpoints
of a segment, then it LIES ON the perpendicular bisector of the segment.
Procedure: 1. prove we have a perpendicular bisector
2. Prove the point is equidistant from the endpoint
3. conclude using LIZON the point lies on the line
 If two lines are parallel, then the alternate exterior angles are congruent.
 If alternate exterior angles are congruent, then the lines are parallel.
 If two lines are parallel, then the corresponding angles are congruent.
 If corresponding angles are congruent, then the lines are parallel.
 If two lines are parallel, then the interior angles on the same side of the
transversal are supplementary.
 If the interior angles on the same side the of transversal are supplementary,
then the lines are parallel.
 If two lines are parallel, then the exterior angles on the same side of the
transversal are supplementary.
 If the exterior angles on the same side the of transversal are supplementary,
then the lines are parallel.
 If two lines are cut by a transversal such that a pair of alternate interior
angles are congruent then the lines are parallel.
 The sum of the measures of the three angles of a triangle is 180°.
 An exterior angle of a triangle is equal to the sum of the measure of the
remote interior angles.
 An exterior angle of a triangle is greater than the measure of each remote
interior angle.
 Midline Theorem – A segment joining the midpoints of two sides of a
triangle is parallel to the third side AND half the length of the third side.
 No Choice Theorem – If two corresponding pairs of angles are congruent
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then the third angle is also congruent. (No Choice + ASA = AAS)
If a quadrilateral has one pair of opposite sides that are both parallel and
congruent then the quadrilateral is a parallelogram.
The sum of the measures of the four angles of a quadrilateral is 360°.
The sum of the interior angles of a n-gon is (n-2)180
The sum of the exterior angles or a n-gon is always 360°
 The number of diagonals in a n-gon is n(n-3)
————
2
 In a regular n-gon, the sum of each interior angle is 180(n-2)
—————
n
 In a regular n-gon, the sum of each exterior angle is 360
———
n
Postulates
 If two parallel lines are intersected/cut by a transversal, then each pair of
alternate interior angles are congruent.
 Parallel Postulate – Through a point not on a given line there exists exactly
one line parallel to the given line.
How to Prove Lines are Parallel:
1. If alternate interior angles are congruent
2. If alternate exterior angles are congruent
3. If corresponding angles are congruent
4. If interior angles on the same side of the transversal are supplementary
5. If exterior angles on the same side of the transversal are supplementary
6. Transitive – If two lines are parallel to the same line then they are parallel.
7. If two lines are perpendicular to the same line then they are parallel.
8. Given
Types of Quadrilaterals
Parallelogram – A quadrilateral with both pairs of opposite sides parallel
 opposite sides are congruent
 opposite angles are congruent
 diagonals bisect each other
 any pair of consecutive angles are supplementary
Rectangle – A parallelogram with one right angle
 opposite sides are congruent
 opposite angles are congruent
 diagonals bisect each other
 any pair of consecutive angles are supplementary
 all of the angles are right angles
 the diagonals are congruent
Rhombus – A parallelogram with two consecutive congruent sides
 opposite sides are congruent
 opposite angles are congruent
 diagonals bisect each other
 any pair of consecutive angles are supplementary
 all of the sides are congruent (equilateral)
 the diagonals bisect the angles of the polygon
 the diagonals are perpendicular bisectors of each other
Square – a rectangle that is also a rhombus
 opposite sides are congruent
 opposite angles are congruent
 diagonals bisect each other
 any pair of consecutive angles are supplementary
 all of the angles are right angles
 the diagonals are congruent
 all of the sides are congruent (equilateral)
 the diagonals bisect the angles of the polygon
 the diagonals are perpendicular bisectors of each other
 the diagonals form four isosceles right triangles
Kite – A quadrilateral with two distinct pairs of consecutive sides are congruent
 one of the diagonals is the perpendicular bisector of the other
Trapezoid – A quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid – A trapezoid with the nonparallel sides congruent
 lower base angles are congruent
 upper base angles are congruent
 diagonals are congruent
 any lower base angle is supplementary to any upper base angle
Test 5
Definitions
Ratio – comparison/quotient of two numbers (ex: 3:2, 3/2)
Proportion – equality of two ratios (ex: 3:2=6:4, 3/2=6/4)
Means – inside numbers (ex: 11:x=2:13 – x and 2 are the means)
Extremes – outside numbers (ex: 11:x=2:13 – 11 and 13 are the extremes)
Mean Proportional (Geometric Mean) – when both means are the same (ex:
11:x=x:5.5 – x is the mean proportional between 11 and 5.5)
Means-Extremes Products Theorem – cross multiply (ex: a/b=c/d equals ad=bc)
Means – Extremes Ration Theorem – ex: if ad=bc then a/b=c/d or d/c=b/a or…
Similar –Two polygons are similar if:
1. the ratios of corresponding sides are equal and
2. all pairs of corresponding angles are congruent
Theorems
 If two polygons are similar, then their perimeters have the same ratio as any
pair of corresponding sides.
 If all three pairs of sides are proportional, then the triangles are similar.
(SSS~)
 If two pairs of corresponding sides are proportional and the pair of included
angles is congruent, then the triangles are congruent. (SAS~)
 CASTC – Corresponding angles of similar triangles are congruent
 CSSTP – Corresponding sides of similar triangles are proportional
 Side Splitter Theorem – If a segment is drawn in a triangle parallel to one
side of the triangle, then it splits the other two sides proportionally.
 Transversal Splitter Theorem – If three or more parallel lines are cut by two
transversals, then the transversals are divided proportionally.
 Angle Bisector Theorem – If a ray bisects and angle of a triangle, then it
divides the opposite side into pieces that are proportional to the other two
sides.
How can you prove that two triangles are similar?
1. AAA
2. AA (no choice theorem)
3. If all three pairs of sides are proportional, then the triangles are similar. (SSS~)
4. If two pairs of corresponding sides are proportional and the pair of included
angles is congruent, then the triangles are congruent. (SAS~)
Test 6
Theorems
 Altitude on Hypotenuse Theorem – If an altitude is drawn to the hypotenuse
of a right triangle, then it divides that right triangle into two smaller triangles
that are similar to each other and similar to the original right triangle.
 Altitude on Hypotenuse Theorem – If an altitude is drawn to the hypotenuse
of a right triangle, then each leg is the mean proportional between the
whole hypotenuse and the adjacent segment.
(c/b = b/x and c/a = b/x)
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Altitude on Hypotenuse Theorem – If an altitude is drawn to the hypotenuse
of a right triangle, then the altitude is the mean proportional between the
segments of the hypotenuse. (x/h = h/y)
Pythagorean Theorem – In a right triangle, the sum of the squares of the
lengths of the legs is equal to the square of the length of the hypotenuse.
(a²+b²=c²)
Converse of Pythagorean Theorem – If a²+b²=c², then triangle ABC is right
(with angle C right).
30-60-90 Triangle Theorem - If a triangle is a 45-45-90 triangle, then the
sides are x, x, x √2.
Converse of 30-60-90 Triangle Theorem - If a triangle's sides are x, x, x √2,
then is is a 45-45-90 triangle.
45-45-90 Triangle Theorem - If a triangle is a 30-60-90 triangle, then the
sides are x, x√3, 2x.
Converse of 45-45-90 Triangle Theorem - If a triangle's sides are x, x√3, x²,
then it is a 30-60-90 triangle.
Pythagorean Triples/Families (integers that satisfy a²+b²=c²)
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
9, 40, 41
x, x, x√2 (45-45-90 triangle)
x, x√3, 2x (30-60-90 triangle)
Rectangular Solid
Faces – 6
Edges – 12
Face Diagonals – 12
Diagonals – 4
Vertices – 8
Regular Square Pyramid
Altitude
Square Base
Vertex
Slant Height
Test 7
Definitions
Circle – The set of all points in a plane that are a given distance away from a point
in the plane. That point is called the center.
Radius – A segment joining the center of the circle to a point of the circle.
Interior – Inside a circle. Its distance from the center is less than the radius.
Exterior – Outside a circle. Its distance from the center is greater than the radius.
Chord – A segment joining any two points of the circle.
Diameter – A chord that passes through the center of the circle.
Arc – Two points on a circle and all the points on the circle between them.
Center of an Arc – The center of the circle of which the arc is a part.
Central Angle – An angle whose vertex is at the center of the circle.
Minor Arc – An arc whose points are on or between the sides of a central angle.
Major Arc – An arc whose points are on or outside a central angle.
Semicircle – An arc of a circle whose endpoints are the endpoints of a diameter.
Measure of a Minor Arc – is the same as the measure of the central angles that
intercepts the arc.
Measure of a Major Arc – is 360° minus the measure of the minor arc with the same
endpoints.
Circumference – 2πr or πd
Arclength – The fractional part of the circumference of the circle.
central angle
2πr
----------------- x
360
Inscribed Angle – An angle in a circle with the vertex on the circle. The measure of
an inscribed angle is equal to half the measure of the intercepted arc.
Secant Line – A line that touches the circle in two points.
Tangent Line – A line that touches the circle in one point.
Point of Tangency/Point of Contact – The point where the tangent line touches the
circle.
Tangent Segment – A segment of a tangent where one of the endpoints is the
point of contact.
Secant Segment – A chord and more on one side only (no limit to external part).
External Part of a Secant Line – The part outside the circle.
Externally Tangent Circles – Touching outside.
Internally Tangent Circles – One inside the other and touching.
Common Tangent (Line) – A line that is tangent to both circles.
Common Internal Tangent (Line) – A line between the two circles. It crosses the
segment connecting the centers.
Common External Tangent (Line) – A line outside the two circles. It does not cross
the segment connecting the centers.
Inscribed – all vertices touch the circle
Circumscribed – all sides are tangent to the circle
Circumcenter of a Circle – The center of a circumscribed (outside) circle. (For a
triangle, the circumcenter is also the point where the three perpendicular bisectors
meet)
Incenter – The center of the inscribed (inside) circle. (For a triangle, the incenter is
also the point where the three perpendicular bisectors meet)
Orthocenter – The point where the three altitudes meet in a triangle.
Centroid – The point where the three medians meet in a triangle (balancing point).
Theorems
 Two circles are congruent if their radii are congruent.
 The distance from the center of a circle to a chord is the measure of the
perpendicular bisector of the chord.
 Two arcs are congruent if their circles are congruent and their central angles
are congruent.
 If a radius bisects a chord, then it is perpendicular to that chord.
 If a radius is perpendicular to a chord, then it bisects that chord.
 The perpendicular bisector of a chord passes through the center of the
circle.
 If two chords of a circle are equidistant from the center, then they are
congruent.
 If two chords are a circle are congruent, then they are equidistant from the
center.
 If central angles are congruent then…
chords are congruent
arcs are congruent
 If chords are congruent then…
arcs are congruent
central angles are congruent
 If arcs are congruent then… chords are congruent
central angles are congruent
 Two Tangent Theorem – If two tangent segments are drawn to a circle from
an external point, then those segments are congruent.
 If the vertex is at the center, then the measure of the angle is equal to the
measure of the arc. (central angle)
 If the vertex is on the circle, then the measure of the angle is equal to half
the measure of the intercepted arc. (inscribed angle, tangent-chord angle)
 If the vertex is inside the circle, then the measure of the angle is equal to the
average of the two intercepted arcs. (chord-chord)
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If the vertex is outside the circle, then the measure of the angle is equal to
half the difference of the two intercepted arcs. (secant-secant, tangentsecant, tangent-tangent)
If two inscribed or tangent-chord angles intercept the same arc, then they
are congruent.
If two inscribed or tangent-chord angles intercept congruent arcs , then they
are congruent.
An angle inscribed in a semicircle is a right angle.
The sum of a tangent-tangent angle and its minor arc is 180°.
If a quadrilateral is inscribed in a circle, then the opposite angles are
supplementary.
If a parallelogram is inscribed in a circle, then it is a rectangle.
Chord-Chord Power Theorem – If two chords intersect (inside a circle), then
the product of the measures of the pieces of one chord is equal to the
product of the measures of the pieces of the other chord.
piece X piece = piece X piece
Tangent-Secant Power Theorem – If a tangent and a secant are drawn to a
circle from the same external point, then the tangent squared is equal to the
product of the whole secant times the external part of the secant.
Secant-Secant Power Theorem - If two secants are drawn to a circle from the
same external point, then product of the whole secant times the external
part of the secant is equal to the product of the whole secant times the
external part of the secant.
Postulates
 A tangent line is perpendicular to the radius drawn to the point of contact.
 If a line is perpendicular to a radius at its outer endpoint, then it is a tangent
line.
Common Tangent Procedure:
1. Draw a segment connecting the centers
2. Draw the radii to the points of contact
3. Mark right angles at points of contact
*4. Through the center of the smaller circle, draw a line parallel to the common
tangent.
5. Look for a rectangle and a right triangle and use the Pythagorean Theorem to
find the missing lengths.
Test 8
Definitions
Area – The number of square units contained within the boundary of the region.
Radius of a Regular Polygon – The radius of a regular polygon is a segment joining
the center to any vertex.
Apothem of a Regular Polygon – The apothem of a regular polygon is a segment
joining the center to the midpoint of any side.
Median of a Trapezoid – The segment connecting the midpoints of the legs of the
trapezoid.
Sector of a Circle – A sector of a circle is a region bounded by two radii and an arc
of the circle.
Segment of a Circle – A segment of a circle is a region bounded by a chord of the
circle and its arc.
Semiperimeter – half the perimeter
Theorems
 Area of a Rectangle – The area of a rectangle equals the product of the base
times the height for that base.
 Area of a Square – The area of a square is equal to the square of a side.
 Area of a Parallelogram – The area of a parallelogram is equal to the product
of the base times the height.
 Area of a Triangle – The area of a triangle equals one half the product of
base times the height (or altitude) for that base.
 Area of a Trapezoid – The area of a trapezoid equals one half of the product
of the height times the sum of the bases.
 Area of a Trapezoid – The area of a trapezoid is the product of the median
by the height.
 Area of a Kite – The area of a kite equals one half the product of its
diagonals.
 Area of an Equilateral Triangle – The area of an equilateral triangle is the
product of one fourth of the square of a side times the square root of three.
 Area of a Regular Polygon – The area of a regular polygon equals one half
the product of the apothem times the perimeter.
 Area of a Circle – The area of the circle is the product of π times the square
of the radius.
 Area of a Sector of a Circle – The area of a sector of a circle is the area of the
circle times the fractional part of the circle determined by the arc.
 Area of a Segment of a Circle – The area of a segment of a circle is the
difference between the area of the sector of the circle and the area of the
triangle.
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The measure of the median of a trapezoid equals the average of the bases.
A median divides a triangle into two triangle with the same area.
If two figures are similar then the ratio of the areas is the square of the ratio
of the corresponding sides.
Hero's Formula – The area of a triangle is the square root of: s(s-a)(s-b)(s-c)
where s=semiperimeter and a,b,c=sides of triangle
Brahmagupta's Formula – The area of an inscribed quadrilateral is the square
root of: (s-a)(s-b)(s-c)(s-d) where s=semiperimeter and a,b,c,d=sides of
inscribed quadrilateral
Distance Formula – square root of: (x1-x2)² + (y1-y2)²
Rectangle
base X height
bXh
Parallelogram
base X height
bXh
Square
1. base X height
bXh
2. side²
s²
Rhombus
1. base X height
bXh
2. ½(diagonal1 X diagonal2)
½(d1 X d2)
Triangle
1. ½(base X height)
½(b X h)
Equilateral Triangle
¼(side²√3)
¼(s²√3)
2. ½(side)(side)(sin of included
angle)
½absinc
3. square root of: s(s-a)(s-b)(s-c)
s=semiperimeter
Trapezoid
1. ½(base1 + base2)(height)
½(b1 + b2)(h)
Kite
½(diagonal1 X diagonal2)
½(d1 X d2)
Regular Polygon
½(apothem)(perimeter)
½ap
2. median X height
mXh
Circle
π(radius)²
πr²
Sector of a Circle
(arc/360)π(radius)²
(arc/360)πr²
Segment of a Circle
area of sector – area of
triangle
Test 9
Definitions
Volume – The area of one slice (base) times the number of slices (height).
Lateral – Around the sides. Everything except for the bases.
x-Axis – A horizontal line through the origin.
y-Axis – A vertical line through the origin.
Origin – Point 0 where two perpendicular lines intersect.
Quadrant – Any one of four regions in which a plane is divided by a pair of
coordinate axes.
Line –A line is made up of points. All lines are straight and extend infinitely far in
both directions.
Slope – rise over run, change in y/change in x, (y1-y2)/(x1-x2), (y2-y1)/(x2-x1)
y-Intercept – If a point lies on the y-axis it has a y-intercept.
x-Intercept – If a point lies on the x-axis it has an x-intercept.
Horizontal Line – y=b, where b is the y-coordinate of every point on the line
Vertical Line – x=a, where a is the x-coordinate of every point on the line
Parallel Lines – Coplanar lines that do not intersect.
Perpendicular Lines – Lines that intersect at right angles.
Circle – The set of all points (on a given plane) that are equidistant from a given
point, called the center.
Locus – Set (location) of all points that contains all the points and only those points
that satisfy specific conditions.
Theorems
 The volume of any prism is equal to the area of the base times the height.
volume = length X width X height
 The surface area of a prism is equal to the sum of the areas of all of the
faces.
 For a pyramid and a cone, the volume is equal to one third the area of the
base times the height.
volume = 1/3 X area of base X height
 The surface area of a cone is equal to the area of the base (area = πr²) plus
the lateral surface area (1/2 circumference times slant height).
surface area = πr² + (1/2 circumference X length)
 The volume of a sphere is equal to 4/3 the area of the circle.
volume = 4/3(πr²)
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The surface area of a sphere is equal to 4 times the area of the circle.
surface area = 4(πr²)
If two lines are parallel, then they have the same slope.
If two lines are perpendicular, then their slopes are negative reciprocals.
Midpoint Formula – If A = (x1, y1) and B = (x2, y2), then the midpoint M(xm, ym)
of line AB can be found by using the averaging process:
M = (xm, ym) = ([½(x1 + x2)], [½( y1 + y2)])
Distance Formula – square root of: (x1-x2)² + (y1-y2)
Equation of a Circle with Center (h,k) – (x-h)² + (y-k)² = r² [when center is
(h,k)]
Equation of a Line – y = mx + b, [when m = slope, b = y intercept]
Point Slope Form for Equation of a Line – y-y1 = m(x-x1), [when m = slope,
(x1,y1) = coordinate of point, y, x = variables]
Tuchman-Schulman Formula – The distance between parallel lines is the
absolute value of the difference between the y intercepts divided by one
plus the square of the slope.
Ib1-b2I / square root of: 1 + m²
How do you find a locus?
1. Find a single point that satisfies the condition(s).
2. Find a second and third point that satisfy the condition(s). Keep finding points
until you see a pattern.
3. Look outside the pattern for points you may have missed. Look within the pattern
for points that should be excluded.
4. Present your answer with a diagram and a verbal description.