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What You Need To Know For Your Geometry SOL Test
Foundations of Geometry A point is a location. It has no size, shape, or thickness.
A line is a series of points extending on a straight path infinitely in opposite directions. It
has length but no width or thickness.
A plane is a flat surface extending infinitely. It has length and width but no thickness.
Collinear points are points that lie on the same line.
Coplanar points are points that lie on the same plane.
The intersection of two lines is a point.
The intersection of two planes is a line.
Parallel lines are coplanar lines that do not intersect.
Parallel planes are two planes that do not intersect.
Skew lines are lines that do not intersect and are not coplanar.
Postulates- statements accepted as true without any proof
Theorems- statements that are proven
Distance Formula
Midpoint Formula
( x2  x1 ) 2  ( y2  y1 ) 2  d
x1 + x2
2
y1 + y2
2
Pairs of Angles
Congruent angles have the same measure.
Adjacent angles share a vertex and a side but have no common interior points.
Linear Pair are two angles in a straight line
Vertical angles are the opposite angles formed by two intersecting lines.
Vertical angles are congruent.
Complementary angles are two angles that add up to 90.
Supplementary angles are two angles that add up to 180.
Constructions –Use a straight edge and a compass
Copy Angle
Copy Line Segment
Bisect Line Segment
Bisect an Angle
Perpendicular form point not on a line
Perpendicular form point on a line
Perpendicular Bisector
Parallel Lines
Inscribed Square
Inscribed Hexagon
Inscribed Triangle
Reasoning & Proofs
The phrase immediately following the word if is the hypothesis. p
The phrase immediately following the word then is the conclusion q
Conditional
Converse
Inverse
Symbols
p→q
q→p
~p→~q
Contrapositive
~q→~p
Biconditional
p  q
To Form
Use the given hypothesis & conclusion
Exchange the hypothesis & conclusion
Replace the hypothesis with its negation and
replace the conclusion with its negation
Replace the hypothesis with its negation and
replace the conclusion with its negation and
switch them
Uses the phrase if and only if. The conditional
statement and its converse are the same.
CIA – Conjuction, Intersection, And, Symbol Λ, read p and q
The conjunction p Λ q is true only when both p and q are true.
Intersection - points that figures have in common –are shared
DUO – Disjunction, Union, Or, Symbol V, read p or q
The disjunction p V q is true if p is true, if q is true, or if both are true.
Union - all points that are contained in either figure
Negation – Not p is the negation of the statement p, Symbol ~ p, read not p
The statements p and ~p have opposite truth values.
Use Venn Diagrams to show these relationships.
p
T
T
F
F
Logic – Truth Values
Conjunction
Disjunction
q
pΛq
p
q
pVq
T
T
T
T
T
F
F
T
F
T
T
F
F
T
T
F
F
F
F
F
Negation
p
~P
T
F
F
T
Inductive Reasoning occurs when you observe individual events and then guess at a general
law. This means you try things many times, observe the results, and then guess at a
general law.
Deductive Reasoning is a system of thought based on statements that have already been
proven or accepted as fact. This is what you do in Geometry.
Law of Detachment – If p, then q.. So if they that p, then q follows.
Law of Syllogism – Get rid of the middleman.
Parallel Lines and Their Relationships
Transversal: a line that intersects two or more lines in a plane at different points.
Alternate Interior s – interior s on opposite sides of transversal
Alternate Exterior s – exterior s on opposite sides of
transversal
Corresponding s – an interior  and an exterior  on the
same side of a transversal
Consecutive Interior s – interior s on the same side of the transversal
Perpendicular Lines
Two lines parallel to perpendicular line
If 2 lines are  to the same line, then lines are .
The distance from a point to a line is measured by the perpendicular segment from the
point to the line.
In a plane, if two lines are equidistant from a third line, then the two lines are parallel to
each other.
Slope Formula
m = y2 – y1
x2 – x1
Parallel lines have the same slope.
Perpendicular lines have slopes - negative reciprocals of each other
Triangles - named according to Congruent Angles
An acute triangle has 3 acute angles.
A right triangle has 1 right angle and 2 acute angles.
An obtuse triangle has 1 obtuse angle and 2 acute angles.
An equiangular triangle has three equal angles.
TRIANGLES - named according to Congruent Sides
A scalene triangle has no congruent sides.
An isosceles triangle has at least 2 congruent sides.
An equilateral triangle has 3 congruent sides.
The sum of the measures of the interior angles of a triangle is 180°.
An Exterior Angle of a Triangle is the angle formed by one side of a triangle and the
extension of another side. The non-straight angle (the one that is not just the extension
of the side) outside the triangle, but adjacent to an interior angle, is an exterior angle of
the triangle.
The measure of the exterior angle of a triangle is equal to the sum of the measures of the
two remote interior angles.
Isosceles Triangle Properties
The congruent sides are the legs. The angle formed by the congruent sides is the vertex
angle.
The angles formed by the base and the congruent sides are the base angles.
If two sides of a triangle are congruent, then the angles opposite those sides are
congruent.
Equiangular Triangle – A triangle is equilateral if and only if it is equiangular.
Each angle of an equilateral triangle is 60.
Triangle Inequality – Largest Side and Largest Angle
Range for length of side of a triangle
Inequalities Involving Two Triangles – SAS, SSS
Triangle Inequality Theorem
Shortest Distance Between a Point and a Line
Inequalities and Triangles
The Exterior Angle Inequality Theorem: If an angle is an exterior angle of a triangle,
then its measure is greater than the measure of either of its corresponding remote
interior angles.
If one side of a triangle is longer than another side, then the angle opposite the longer
side has a greater measure than the angle opposite the shorter side.
The converse is also true: If one angle of a triangle has a greater measure than another
angle, then the side opposite the greater angle is longer than the side opposite the lesser
side.
Note: The largest angle of a triangle will always be opposite a largest side, and the
smallest angle will always be opposite the shortest side.
The Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the length of the
third side. This theorem can be used to determine whether 3 segments will form a
triangle.
The perpendicular segment from a point to the line is the shortest segment from the
point to the line.
The perpendicular segment from a point to a plane is the shortest segment from the point
to the plane.
Inequalities Involving Two Triangles
The SAS Inequality aka Hinge Theorem: If two sides of a triangle are congruent to two
sides of another triangle and the included angle of one triangle has a greater measure
than the included angle in the other triangle, then the third sides of the first triangle is
longer than the third side of the second triangle.
The SSS Inequality: If two sides of a triangle are congruent to two sides of another
triangle and the third side in one triangle is longer than the third side in the other
triangle, then the angle between the pair of congruent sides in the first triangle is
greater than the corresponding angle in the second triangle.
Note: If you have an angle included between two sides, then the longer side will always be
opposite a larger angle and a shorter side will always be opposite a smaller angle.
Congruent Triangles
Triangles that have exactly the same size and shape are called congruent triangles.
Proving Congruence – SSS, SAS, ASA, AAS, and HL
Congruent Triangles- Name Corresponding Parts
Triangles and Their Relationships
Concurrency
When three or more concurrent lines (or rays or segments) intersect in the same point,
then they are called concurrent lines (or rays or segments). The point of intersection of
the lines is called the point of concurrency.
Medians
A median is a line segment whose endpoints are a vertex of a triangle and the midpoint of
the side opposite the vertex.
The intersection of the medians of a triangle is called the centroid. The centroid is
located two-thirds of the distance from a vertex to the mid-point of the side opposite
the vertex on a median.
Angle Bisectors
Any point on an angle bisector is equidistant from the sides of the angle.
Any point on the interior of an angle that is equidistant from the sides of the angle lies on
the angle bisector.
The intersection of the angle bisectors of a triangle is called the incenter. The incenter
of a triangle is equidistant from the sides of the triangle.
Altitudes
An altitude of a triangle is a segment perpendicular to a side of the triangle that has a
vertex as one endpoint and a point on the line containing the side opposite the vertex as
the other endpoint.
The intersection of the altitudes of a triangle is called the orthocenter.
A perpendicular bisector of a side of a triangle is a line, segment, or ray that passes
through the midpoint of the side and is perpendicular to that side. Any point on the
perpendicular bisector of a segment is equidistant from the endpoints of the segment.
The intersection of the perpendicular bisectors of a triangle is called the circumcenter.
The circumcenter is equidistant from the vertices of the triangle.
Similarity
Similar figures have the same shape. They may or may not have the same size.
Two polygons are similar if
1) corresponding angles are congruent and the
2) lengths of corresponding sides are proportional.
The symbol ~ is used to indicate similarity.
Congruent polygons are a special type of similar polygons, the ratio of the corresponding
sides is 1:1
If the ratio of two similar figures is a:b, then
1) a:b is the ratio of their perimeters **
There are three ways to prove that two triangles are similar.
AA Similarity
If two angles of one triangle are congruent to the two angles of another triangle,
then the triangles are similar.
SSS Similarity
If the corresponding sides of two triangles are proportional, then the triangles are
similar.
SAS Similarity
If an angle of one triangle is congruent to an angle of a second triangle and the lengths
of the sides including these angles are proportional, then the triangles are similar.
Right Triangles
The geometric mean of two positive numbers a and b is the positive number x such that
a:x = x:b is true.
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles
formed are similar to the original triangle and to each other.
SLeg
1
LLeg
√3
Hyp
2
** In a right triangle, the altitude from the
right angle to the hypotenuse divides the
hypotenuse into two segments. The length of the
altitude is the geometric mean of the lengths of the two segments.
** In a right triangle, the altitude from the right angle to the hypotenuse divides the
hypotenuse into two segments. The length of each leg of the right triangle is the
geometric mean of the lengths of the hypotenuse and the segment of the
hypotenuse that is adjacent to the leg.
Pythagorean Theorem and Converse
In a right triangle, the square of the length of the hypotenuse is equal to the sum of
the squares of the legs.
c2 = a2 + b2
If c2 > a2 + b2 the triangle is obtuse.
If c2 < a2 + b2 the triangle is acute.
Special Right Triangles 30 – 60 – 90i
In a 30°- 60°- 90° triangle, the hypotenuse is twice as long as the shorter leg, and the
longer leg is √3 times as long as the shorter leg
Special Right Triangles
45 – 45 – 90
In a 45°- 45°- 90° triangle, the hypotenuse is √2 times as long as each leg. The ratio of
the sides is 1:1:√2.
Leg
1
Leg
1
Hyp
√2
Trigonometry Ratios –
A trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
The word trigonometry is derived from the ancient Greek language and means
measurement of triangles. The three basic trigonometric ratios are sine, cosine,
and tangent, which are abbreviated as sin, cos, and tan respectively.
Sin A = side Opposite A
Hypotenuse
Cos A = side Adjacent to A
Hypotenuse
Tan A = side Opposite A
side Adjacent to A
Angles of Elevation & Depression
The angle that your line of sight makes with a line drawn horizontally is called the angle
of elevation or the line of depression.
Quadrilaterals
Name of Regular
Polygons
No of
Sides
No of
Diagonals
from
vertex
No of
Triangle
s
Formed
Sum of
Interior
Angles
Each
Interior
Angle
Sum of
Exterior
Angles
Triangle
3
-
-
180
60
360
Quadrilateral
4
1
2
360
90
360
Pentagon
5
2
3
540
108
360
Hexagon
6
3
4
720
120
360
Heptagon
7
4
5
900
128.6
360
Octagon
8
5
6
1080
135
360
Nonagon
9
6
7
1260
140
360
Decagon
10
7
8
1440
144
360
Icosagon
20
17
18
3240
162
360
n
n - 3
n - 2
180(n – 2)
n-gon
180(n – 2)
n
360
The Interior Angle Sum Theorem states that if a polygon has n sides and S is the sum
of the measures of its interior angles, then S = 180(n – 2). This equation can be used to
find the measures of each interior angle in a regular polygon. Also, it can be used to find
the number of sides in a polygon, if the sum of the interior angles measures is known.
An Exterior Angle of a polygon is an angle formed by one side and a ray extending out
from an adjacent side.
The Exterior Angle Sum Theorem states that the sum of the exterior angles of a
convex polygon is always 360° no matter how many sides the polygon has.
The Measure of each Exterior Angle of a regular polygon is 360° .
N
A quadrilateral is a polygon of four sides.
A parallelogram is a quadrilateral whose opposite sides are parallel and congruent.
A rectangle is a parallelogram with four right angles.
A rhombus is a parallelogram with four congruent sides.
A square is a rectangle with four congruent sides or a rhombus with four right angles.
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
A kite is a quadrilateral with two pairs of adjacent congruent sides.
QUADRILATERALS classified by the number of PARALLEL SIDES
A parallelogram, rectangle, rhombus, and square each have two pairs of parallel sides.
A trapezoid has only one pair of parallel sides.
A kite has no parallel sides.
QUADRILATERALS classified by the measures of the ANGLES
A rectangle and a square have four 90 angles.
A trapezoid and a kite may have none, one or two 90 angles.
QUADRILATERALS classified by the OPPOSITE ANGLES
A parallelogram, rectangle, rhombus, and a square have 2 pairs of congruent opposite
angles.
A kite has 1 pair of congruent opposite angles
QUADRILATERALS classified by CONSECUTIVE ANGLES
A parallelogram, rectangle, rhombus, and a square have 4 pairs of supplementary
consecutive angles.
An isosceles trapezoid has 2 pairs of supplementary consecutive angles.
QUADRILATERALS classified by the number of CONGRUENT SIDES
A parallelogram and a rectangle have two pairs of opposite congruent sides.
A rhombus and a square have four congruent sides.
QUADRILATERALS with OPPOSITE SIDES CONGRUENT
A parallelogram, rectangle, rhombus, and a square have two pairs of opposite sides
congruent.
An isosceles trapezoid has one pair of congruent sides.
QUADRILATERALS with ADJACENT SIDES CONGRUENT
A kite has exactly two pairs of adjacent sides congruent.
QUADRILATERALS and properties of the DIAGONALS
Each diagonal of a parallelogram divides it into two congruent triangles.
The diagonals of a rectangle and a square are congruent.
The diagonals of a parallelogram, rectangle, and a square bisect each other.
The diagonals of a rhombus and a square bisect a pair of opposite angles.
The diagonals of a rhombus, square, and a kite are perpendicular to each other.
One of the diagonals of a kite bisects the angles at its endpoints.
One of the diagonals of a kite bisects the other diagonal.
SQUARE
A square is a special type of both a rectangle and a rhombus.
TRAPEZOID
A trapezoid has one pair of parallel sides which are called the bases. The non-parallel
sides are called the legs. A base angle is formed by a leg and a base.
The segment that joins the midpoints of the legs is the median aka midsegment. The
median is parallel to the bases and its measure is ½ the sum of the measure of the two
bases.
If the legs are congruent, then the trapezoid is an isosceles trapezoid. The base angles
are congruent and the diagonals are congruent.
If a base angle is a right angle, then the trapezoid is a right trapezoid.
KITE
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
A kite has two pairs of adjacent congruent sides. The diagonals are perpendicular to each
other. One of the diagonals bisects the angles at its endpoints. It bisects the other
diagonal.
4 Sides
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Exactly 2 pairs of Parallel Sides
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Only 1 pair of Parallel Sides
0 pairs of Parallel Sides
2 pairs opposite sides are congruent
All sides are congruent
Exactly 2 pairs of adjacent sides congruent
Opposite angles are congruent
Only 1 pair of opposite angles congruent
All angles are congruent -right angles
4 pairs consecutive angles - supplementary
2 pairs consecutive angles -supplementary
Diagonals bisect each other
Only 1 diagonal bisects the other diagonal
Diagonals are congruent
Diagonals are perpendicular
Diagonals bisect pair opposite angles
1 Diagonal bisects angles at its endpoints
Sum of the angles is 360
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Isos
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CIRCLE - a set of points equidistant from one fixed point.
A circle is named by its center point.
A chord is a segment with endpoints on the circle.
A diameter is a chord that passes through the center of the circle.
A radius is any segment with one endpoint at the center of the circle and the other
endpoint on the circle.
A radius is 1/2 the length of the diameter.
Circumference of a circle is the distance around the circle.
C = 2πr or C = πd
Perimeter - is the distance around a polygon
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A central angle of a circle has the center of the circle as its vertex, and its sides are two
radii of the circle.
The sum of the measures of the central angles of a circle with no interior points in
common is 360.
A central angle separates the circle into two parts – each of which is an arc.
The measure of each arc is related to the measure of its central angle.
A minor arc degree measure equals the central angle and is less than 180.
A major arc degree measure equals 360 minus the measure of the minor arc and is greater
than 180.
A semicircle is an arc and measure 180.
In the same or congruent circles, two arcs are congruent if and only if their corresponding
central angles are congruent. Two angles are congruent if and only if the corresponding
central angles are congruent.
There are 2 ways to measure an arc:
1) Angles have degree measure, similarly, arc have degree measure. In a circle graph, the
central angles divide the circle into wedges often expressed by percents. The size of the
angle is proportional to the percent. Multiply the percent by 360 to determine the
measure of the central angle.
2) Arc Length is part of the length of the circumference of the circle. Use a proportion.
Degree measure of arc
=
arc length
Degree measure of whole circle
circumference
The endpoints of a chord are also endpoints of an arc.
In a circle or congruent circles, two minor arcs are congruent if and only if their
corresponding chords are congruent.
In a circle or congruent circles, two chords are congruent if and only if they are
equidistant from the center of the circle.
The chords of adjacent arcs can form a polygon. This polygon is inscribed in the circle
because all of its vertices lie on the circle. The circle circumscribes the polygon.
Diameters that are perpendicular to chords create special segments and arc relationships.
In a circle, if a diameter or radius is perpendicular to a chord, then it bisects the chord
and its arc.
Inscribed Angles
An inscribed angle is an angle that has its vertex on the circle and its sides contained in
chords of the circle.
If an angle is inscribed in a circle, then the measure of the angle equals one-half of the
intercepted arc (or the measure of the angle).
Inscribed polygons also have special properties. An inscribed triangle with a side that is a
diameter is a special type of triangle.
If an inscribed angle intercepts a semicircle, the angle is a right angle.
If a quadrilateral is inscribed ina circle, then its opposite angles are supplementary.
Tangents
A tangent intercepts a circle in exactly one point. This point is called the point of
tangency. If a line is tangent to a circle, then it is perpendicular o radius drawn to the
point of tangency.
More than one line can be tangent to the same circle. If two segments from the same
exterior point are tangent to a circle, then they are congruent.
If a circle is inscribed in a polygon, then every ides of the polygon is tangent to the circle.
Secants, Tangents, and Angle Measures
A line that intersects a circle in exactly two points is a secant.
If two lines intersect a circle, there are three (3) places where the lines can intersect.
If a tangent and a chord intersect at a point ON a circle, then the measure of each angle
formed is one half the measure of its intercepted arc.
If two chords intersect in the INTERIOR of a circle, then the measure of each angle is
1/2 the sum of the measures of the arcs intercepted by the angle and its vertical angle.
If a tangent and a secant, two tangents or two secants intercept in the EXTERIOR of a
circle, then the measure of the angle formed is one half the difference of the measures
of the intercepted arcs.
Special Segments in a Circle
When two chords intersect in the interior of a circle, each chord is divided into two
segments which are called segments of a chord. The following theorem gives a
relationship between the lengths of the four segments that are formed.
If two chords intersect in the interior of a circle, then the product of the lengths of the
segments of one chord is equal to the product of the lengths of the segments of the
other chord.
If two secant segments share the same endpoint outside a circle, then the product of the
length of one secant segment and the length of its external segment equals the product of
the length of the other secant segment and the length of its external segment.
If a secant segment and a tangent segment share an endpoint outside a circle, then the
product of the length of the secant segment and the length of its external segment equal
the square of the length of the tangent segment.
Equations of Circles
You can write an equation of a circle if you know its radius is r and the center is (h, k).
(x – h)2 + (y – k)2 = r2
Transformations
When a shape can be mapped, folded, or rotated onto itself, then it has symmetry.
A figure can have one or both of two basic symmetries.
1) A figure that folds onto itself has reflectional symmetry.
A figure can have none, 1 or more lines of symmetry.
A figure has rotational symmetry if there is a rotation of 180 or less that maps the
figure onto itself. Point symmetry is when a figure has a rotational symmetry of 180.
A figure can have none, 1 or more than one rotational symmetry.
Some of these figures have a point that is a common point of reflection for all points on
the figure. This common point of reflection is called a point of symmetry and it is the
midpoint of all segments between the preimage and image points.
A shape has rotational symmetry when the image is rotated (around the center point) so
that it appears 2 or more times. The shape can be rotated and it still looks the same.
Figures in a plane can be reflected, rotated, translated, or dilated to produce new
figures.
The original figure is the preimage and the new figure is called the image.
Isometries produce images that are congruent to their preimage.
ReFLection - FLip the figure over a point, a line (the x-axis, y-axis, a line parallel to the x
or y-axis, or y = x) or a plane. The image and the preimage are congruent.
A shape has line symmetry when one half of it is the mirror image of the other half.
Each point on the reflected image is the same distance from the line as the corresponding
point in the original figure.
Figures that are commonly called symmetrical have a line of reflection, or line of
symmetry. It can be folded along the line of symmetry so that the two halves match.
TranSLation - SLide the figure
All the points on the figure move the same distance in the same direction.
A translation slides a figure a units horizontally and b units vertically, in symbols,
(x, y) → (x + a, y + b).
RoTation - Turn the figure about a point either clockwise or counterclockwise using 90
increments. If not stated, rotate the figure counterclockwise.
The fixed point is called the center of rotation. The fixed point may or may not be on the
figure.
Original figure
(x, y)
st
1 counter clockwise rotation 90
(x, y) → (- y, x)
nd
2 rotation 180
(x, y) → (- x, - y)
rd
3 counter clockwise rotation 270
(x, y) → ( y, - x)
Dilations - changes the size of the figure by shrinking or enlarging it.
A
dilation is NOT an isometry because it does not produce an image congruent to the
preimage.
A dilation requires a center point (C) and a scale factor (r).
The scale factor = image length
preimage length
r is a positive number such that r = image
and r  1.
preimage
Dilations that make the figures larger have a scale factor greater than 1. A dilation is a
reduction if 0 < r < 1.
Dilations that make the figures smaller have a scale factor less than 1. A dilation is an
enlargement if r > 1.
A dilation changes the size of a figure by a scale factor to create a similar f
Area, Surface Area, & Volume
Area
Parallelogram - The area of a parallelogram is the product of a base and height.
Rectangle—The area of a rectangle is the product of its base and height.
Triangle—The area of a triangle is one half the product of a base and height.
Trapezoid—The area of a trapezoid is one half the product of the height and the sum of
the bases.
A = ½ h(b1 + b2)
Rhombus—The area of a rhombus is one half the product of the lengths of the diagonals.
A = ½ d1 d2
Circle – The area of a circle is  times the square of the radius or A = r2.
A Sector of a Circle is a region bounded by two radii of the circle and their intercepted
arc
Sector of circle is part of the area of the circle. Use a proportion.
Degree measure of arc
=
Sector
Degree measure of whole circle
Area of Circle
The apothem is the height of a triangle between the center and two consecutive vertices
of the polygon.
you can find the area o any regular n-gon by dividing the polygon into congruent triangles
A = Area of 1 triangle • # of triangles
= ( ½ • apothem • side length s) • # of sides
= ½ • apothem • # of sides • side length s
= ½ • apothem • perimeter of a polygon
This approach can be used to find the area of any regular polygon.
The area of a regular n-gon with side lengths (s) is half the product of the apothem (a)
and the perimeter (P), so
A = ½ Pa
Three Dimensional Figures
A prism is a solid figure having two congruent parallel polygonal bases. The faces
connecting the corresponding edges of the bases are rectangles. A prisms is classified by
the shape of the bases.
SA of prism = 2lw + 2wh + 2lh
V of prism = lwh
A pyramid is a solid figure whose base is a polygon and triangular faces that all share a
common vertex. A pyramid is classified by the shape of its base.
SA of pyramid = ½ pl + B
V of pyramid = 1/3 Bh
A cylinder is a solid figure having two congruent circular bases. The lateral surface
unrolls into a rectangle, two of whose edges is the circumference of the circular base and
the other two are the height of the cylinder.
SA of cylinder = 2πrh + 2πr2
V of cylinder = πr2h
A cone is a solid figure whose base is a circle with a curved surface of line segments that
connect the points on the base to the vertex.
SA of cone = πr2+ πrl
V of cone = 1/3 r2h
Surface Area and Volume of Spheres
A sphere is the locus of points in space that are a given distance from a point.
The point is called the center of the sphere. A radius of a sphere is a segment from the
center to a point on the sphere.
A chord of a sphere is a segment whose endpoints are on the sphere
A diameter is a chord that contains the center. As with all circles, the terms radius and
diameter also represent distances, and the diameter is twice the radius.
The surface area of a sphere with radius r is S = 4r2.
The volume of a sphere with radius r is S = 4r3.
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Similar Solids
If the ratio of two similar figures is :b, then
1) a:b is the ratio of their perimeters
2) a2:b2 is the ratio of their areas
3) a3:b3 is the ratio of their volumes