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the distance postulate
to every pair of different points there corresponds a unique positive number
Postulate 1: The Ruler Postulate
Once a coordinate system has been chosen, the distance between any two points is the absolute value of the difference of the corresponding coordinates
The Ruler Placement Postulate
Given two points P and Q on a line, P is zero and the coordinate of Q is positive
Every plane contains (points)
at least three noncollinear points
Space contains (points)
at least four noncollinear points
IF two points on a line lie in a plane, then the line...
lies in the same plane.
If two planes intersect their intersection is a
line
The Area Postulate
To every polygonal region there corresponds a unique positive real number
The Congruence Postulate
If two triangles are congruent then their triangular regions have the same area.
The Area Addition Postulate
If two polygonal regions intersect only in edges and vertices (or do not intersect at all) then their area is the union of the sum of their areas.
If A B and C are three different points of the same line then exactly one of them is
in between the other two
Given a line and a point not on the line
there is exactly one plane containing both.
Given two intersecting lines
there is exactly one plane containing it.
If two angles are complementary then they are
acute angles
If two angle are congruent and supplementary then each is a
right angle
If two intersecting lines form one right angle
then they form four right angles
Theorem: Angle Bisector Theorem
Every angle has exactly one bisector
Theorem: The Isosceles Triangle theorem
If two sides of a triangle are congruent then the angles opposite them are congruent.
Theorem: Converse Isosceles Triangle Theorem
If two angles of a triangle are congruent then the sides opposite them are congruent
Theorem: The Perpendicular Bisector Theorem
The perpendicular bisector of a segment in a plane is the set of all points of the plane that are equidistant from the end points of the segment
Theorem: Parts theorem
the part is smaller than the whole
Theorem: The Exterior angle theorem
exterior is greater than remote. In fact, exterior is the sum of the two remote.
If two angles of a triangle are not congruent then the sides
are not congruent
if a line and a plane are perpendicular then the plane contains every line
perpendicular to the given point at its intersection with the given plane
How do you know if a number is divisible by 10?
If the number ends in a 0.
How do you know if a number is divisible by 7?
If you remove the last digit of the number, double it, and subtract it from the remaining digits and the result is divisible by 7.
In a right triangle, what do the two acute angles equal up to?
90 degrees, they are complementary.
In a parallelogram, the opposits are what?
The opposit sides are parallel, and the opposit angles are congruent.
In a rectangle, what are the angles?
All are 90 degrees, and opposite sides are congruent as are diaganols.
In a rhombus, what are the angles?
Opposite angles are congruent as are opposite sides. The diaganol is perpendicular.
How do you calculate the circumference of a circle?
C = 2*pi*r = pi*d
How do you calculate the area of a circle?
A = pi*r^2
What Property does this represent?
a+b = b+a
commutative property of addition
What Property does this represent?
a*b = b*a
Commutative Property of Multiplication
What Property does this represent?
a+(b+c) = (a+b)+c
Associative Property of Addition
What Property does this represent?
a*(b*c) = (a*b)*c
Associative Property of Multiplication
What Property does this represent?
a*(b+c) = a*b+a*c
The distributive property of multiplication over addition
What Property does this represent?
a*(b-c) = a*b-a*c
The distributive property of multiplication over division
How do you know if a number is divisible by 2?
If the number is even.
How do you know if a number is divisible by 3?
If the sum of the individual digits of the number is divisible by 3.
How do you know if a number is divisible by 4?
If the last two digits, taken as a two-digit number, are divisible by 4.
How do you know if a number is divisible by 5?
If the last digit of the number is a 5 or a 0.
How do you know if a number is divisible by 8?
If the last three digits, taken as a three-digit number, are divisible by 8.
How do you know if a number is divisible by 9?
If the sum of the individual digits of the number is divisible by 9.
How do you know if a number is divisible by 6?
If it is divisible by both 2 and 3.
How do you know if a number is divisible by 12?
If it is divisible by both 3 and 4.
What is the new figure called after you transform a figure?
image
What is a prediction based on inductive reasoning?
conjecture
What parts does a conditional statement have?
"hypothesis and conclusion"
What is a conditional statement called when the hypothesis is true and the conclusion is false?
counterexample
What is a line, segment, or ray that intersects a segment at its midpoint?
bisector
What is the point that divides a segment into 2 congruent segments called?
midpoint
What is a part of a line with no endpoint called?
ray
What is a part of a line with 2 endpoints called?
segment
What do you call an angle that measures 180 degrees?
straight angle
Name how many congruent sides each triangle has: scalene, isoceles, equilateral.
s - none
i - two
e - all
How many acute angles does an acute triangle have?
3
What do you call a closed plane figure whose sides are segments that intersect only at their endpoints?
polygon
What does being a "regular" polygon mean?
"equilateral
What is the sum of the exterior angles of any polygon?
360 degrees
What type of reasoning uses facts?
deductive
What do you call a statement that is accepted without proof?
postulate
What is a conjecture that can be proved to be true?
theorem
What's the formula for the equation of a line?
y = mx + b
What's the equation of a circle with center (0,0)?
X2 + Y2 = R2
What's the equation of a circle with a center that is not (0,0)?
(x-h)2 + (y-k)2 = r2
What do you call two circles that have the same center?
concentric circles
What do you call (x,y,z)?
an ordered triple
Corresponding angle __________
postulate
Alternate Interior Angle __________
Theorem
Name the theorem: if 2 planes are intersected by a third plane, then the lines of intersection are parallel.
intersecting planes theorem
Name the Pythagorean Theorem formula.
(A)2 + (B)2 = (C)2
What are the two parallel sides of a trapezoid called?
bases
What are the two non-parallel sides of a trapezoid called?
legs
Theorem: The Pythagorean Theorem
The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
Theorem: The Triangle Angle Sum Theorem.
The sum of the angles of a triangle is 180 degrees.
Theorem: Diameter of a circle
If the diameter of a circle is "d", its circumference is pi(d)
Theorem: Radius of a circle
If the radius of a circle is "r", its area is pi times r squared.
Theorem: The angles in a linear pair
The angles in a linear pair are supplementary.
Theorem
Perpendicular lines form...
Perpendicular lines form right angles.
Theorem
Vertical angles
Vertical angles are equal.
Corollary to the Ruler Postulate
A line segment has exactly one midpoint.
Corollary to the Protractor Postulate.
An angle has exactly one ray that bisects it.
Corollary to the definition of a right angle.
All right angles are equal.
Theorem 8: If the angles in a linear pair are equal...
If the angles in a linear pair are equal, then their sides are perpendicular.
Definition: Supplementary
Two angles are supplementary if their sum is 180 degrees.
Definition: Complementary
Two angles are complementary if their sum is 90 degrees. Each angle is called the COMPLEMENT of the other.
What is a corollary?
A corollary is a theorem that can be easily proved as a consequence of a postulate or another theorem.
Definition: midpoint of a line segment
A point is the midpoint of a line segment iff it divides the line segment into two equal segments.
Definition: bisects an angle
A line bisects an angle iff it divides the angle into two equal angles.
Congruent
coinciding exactly when superimposed.
Definition: (Betweeness of Points)
A point is between two other points on the same line iff its coordinate is between their coordinates. ( A-B-C iff a<b<c or a>b>c.)
The Reflexive Property
a = a (Any number is equal to itself)
The Substitution Property
If a = b, then a can be substituted for b in any expression.
The Addition Property
If a = b, then a + c = b + c.
The Subtraction Property
If a = b,then a - c = b - c
The Multiplication Property
If a = b, then ac = bc
The Division Property
If a = b and c does NOT = 0, then a divided by c = b divided by c.
The Distributive Rule
"relates the operations of multiplication and addition. For any numbers a, b, and c,
Postulate
A postulate is a statement that is assumed to be true without proof.
Direct proof
"If a, then b.
Conditional statements
A conditional statement consists of two clauses, one of which begins withthe work "if" or "when" or some equivalent word.
Hypothesis
If a, then b. The letter a represtns the "if" clause, or hypothesis.
Conclusion
If a, then b. The letter b represents the "then" clause, or conclusion. (The word "then" is often omitted.)
Converse
The converse of a conditional statement is found by interchanging the hypothesis and conclusion. The converse of "if a then b" is "if b then a"
Is the converse always true?
The converse may or may not be true, however the converse of a definition is always true.
Theorem
A theorem is a statement that is proved by reasoning deductively from already accepted statements.
Premises of the argument
The statements "if a then b, if b then c, ...."
Conclusion of the argument
If a then n. The conclusion might be considered a theorem.
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees. m<A+m<B+m<C=180
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m<1=m<A+m<B
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary. m<A+m<B=90
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. if <A=<D & <B=<E, then <C=<F
Properties of Congruent Triangles (Reflexive, Symmetric, Transitive)
"REFLEXIVE: Every triangle is congruent to itself.

TRANSITIVE: if <ABC=<DEF & <DEF=<JKL, then <ABC=<JKL"
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Postulate (21)
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
Base Angle Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
Converse of the Base Angles Theorem
If two angles of a triangle are congruent, then the sides oppsite them are congruent.
Corollary to the Base Angles Theorem (4.6)
If a triangle is equilateral, the it is equiangular.
Corollary to the Converse of the Base Angles Theorem
If a triangle is equinangular, then it is equilateral.
Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.
Longer Side Theorem
If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.
Largest Angle Theorem
If one angle of a traingle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
Exterior Angle Inequality
The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle isreater than the length of the third side.
Definition: Noncoplanar Points
Points that are not all on the same plane
Postulate 2: Segment Addition Postulate
If B is between A and C then,
AB + BC = AC
Definition: Vertex
the common end point of two rays that form an angle
Definition: Acute Angle
an angle that is less than 90 degrees
Definition: Obtuse Angle
an angle that is greater than 90 degrees
Postulate 3: Protractor Postulate
consider opposite rays OA and OB.
. There lies rays between them paired with real numbers 0 to 180
. the angle of the two rays is the absolute value of between the paired rays
Postulate 4: Angle Addition Postulate
AOC = AOB + BOC
and
if AOC is a straight line, then AOB + BOC = 180
Definition: Adjacent Angles
angles that have a common side and vertex (i.e they are beside each other)
Definition: bisector of an angle
a ray that divides exactly the angle into two congruent angles
Postulate 5: Line, Plane, Space
- a line contains at least 2 points
- a plane contains at least 3 points not on the same line (noncollinear)
- space contains at least 4 noncoplanar points
Postulate 6: One Line
through any two points there is exactly one line
Postulate 7: One Plane
- through any three noncollinear points there is one plane, and
Postulate 8: Line in a Plane
if two points are in a plane then the line that contains the two points is in that plane
Postulate 9: Intersecting Planes
if two planes intersect , then their intersection is a line
Theorem 1-1 (intersecting lines)
if two lines intersect then they intersect in exactly one point
Theorem 1-2 (Line and a Point)
through a line and a point not on the line there lies exactly one plane
Theorem 1-3 (line intersecting)
if two lines intersect, then exactly one plane contains both lines.
Two rays with the same endpoint form what?
an angle
Congruent segments have equal what?

Congruent angles have equal what?
lenghts

angles
Angles are classified into what definitions? (4)
acute
right
obtuse
straight
Statements that are accepted without proof are called?

Statements that are proved are called?
postulates

theorems
What are two other terms used for "if-then statements"
conditional statements or,

conditionals
If p, then q

what is 'p' and 'q' called
p - hypothesis

q - conclusion
the converse of 'If p, then q' is?
if q, then p
Symetric Property is?
if a=b, then b=a
Transitve Property
if a=b and b=c, then a=c
Reflexive Property
(Property of Congruence)
DE = DE

angle D = angle D
Symetric Property
(property of Congruence)
if DE=FG, then FG=DE

if angle D=F then angle F=D
Transitive Property
(property of Congruence)
if DE=FG, and FG=JK, then DE=JK

if angleD = angleE, and angle E = angleF, then angleD = angleF
Theorem 2-1: Midpoint Theorem
If M is the midpoint of AB, then AM = 1/2AB and MA = 1/2AB
Theorem 2-2: Angle Bisector Theorem
if BX is the bisector of ABC, then ABX = 1/2 ABC and XBC = 1/2ABC
What are the Reasons used in Proofs? (4)
Given Information
Definitions
Postulates
Theorems
Theorem 2-3: Vertical Angles
Vertical angles are Congruent
Definition: Perpendicular lines
if JK is perpendicular to MN, then each of the numbered angles is a right angle

if any one of the numbered angles is a right angle, then JK is perpendicular to MN
Theorem 2-4: if two lines are perpendicular
if two lines are perpendicular, then they form congruent adjacent angles
Theorem 2-5: If two lines form congruent adjacent angles
then the lines are perpendicular
Theorem 2-6: if the exterior sides of two adjacent acute angles are perpendicular
then the angles are complementary
Theorem 2-7: If two angles are supplements of congruent angles then,
the angles are also congruent
Theorem 2-8: If two angles are complements of congruent angles then
the angles are also congruent
Definition: Parallel lines
are coplanar lines that do not intersect
Definition: Skew Lines
are non coplanar, that is:
they do not intersect and are not parallel
Theorem 3-1: if two parallel planes are cut by a third plane then,
the lines of intersection are parallel
Definition: Transversal line
a line that intersects two or more coplanar lines at different points
Picture Page 74:
what are the:
Alternate interior angles?
Same Side Interior angles?
Corresponding angles?
3 and 6, 4 and 5

3 and 5, 4 and 6

1 and 5, 2 and 6, 3 and 7, 4 and 8
Postulate 10: If parallel lines cut by a transversal then,
the corresponding angles are congruent
Theorem 3-2: if two parallel lines are cut by a transversal, then
alternate interior angles are congruent
Theorem 3-3: If two parallel lines are cut by a transversal, then
same side interior angles are supplementary
Theorem 3-4: If a transversal is perpendicular to one of two parallel lines then
it is perpendicular to the other one also
Postulate 10: If two parallel lines are cut by a transversal then
the corresponding angles are congruent
Postulate 11: If two lines are cut by a transversal and corresponding angles are congruent then
the lines are parallel
Theorem 3-6: If two lines are cut by a tranversal and same-side interior angles are supplementary then
the lines are parallel
Theorem 3-7: In a plane two lines perpendicular to the same line are
parallel
Theorem 3-8: Through a point outside a line, there is exactly one line
parallel to the given line
Theorem 3-9: Through a point outside a line, there is exactly one line that is
perpendicular
Theorem 3-10: Two lines parallel to a third line are
parallel to each other
Theorem 3-11: The sum of the measure of the angles of a triangle is

What is Corollary 1, 2, 3, 4?
180

C1 - if two angles of one triangle are congruent to two angles of another triangle, the third angles are also congruent

C2 - each angle of an equiangular triangle has a measure of 60

C3 - in a triangle there can be at most one right or obtuse angle

C4 - the acute angles of a right triangle are complementary
Theorem 3-12: The measure of an exterior angle equals the sum of the measures of
the two remote interior angles
Theorem 3-13: The sum of the measures of the angles of a convex polygon with N sides is? (formula)
(N-2)*180
How do you find the sum of the interior angles of a polygon?
draw diagonals from one vertex only to divide the polygon into triangles
Definition: what is formed by drawing a segment from one vertex to any nonconsecutive vertex
a diagonal
Theorem 3-14: The sum of the measures of the exterior angles of any convex polygon, one at each vertex is?
360
Definition: Deductive Reasoning (2)
- conclusion is based on accepted statements

- conclusion must be true id hypotheses are ture
Definition: Inductive Reasoning
- conclusion is based on several past observations

- conclusion is probably true, but not necessarily true
Name three ways to prove triangles are congruent (3 postulates)
SSS

SAS

ASA
How can you prove that two segments or two angles are congruent if triangles are involved (3 steps)
1. identify two triangles in which two segments or angles are corresponding then,

2. Prove the triangles are congruent

3. state that if two parts are congruent, then the other parts are using reasoning and postulates
Theorem 4-1: The Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are?

Corollary 1, 2, 3
congruent

C1 - an equilateral triangle is also equiangular

C2 - an equilateral trianle has three angles of 60 degrees

C3 - the bisector of the vertex angle of an isosceles ttriangle is perpendiclar to the base at its midpoint
Theorem 4-2: if two agnles of a triangle are congruent, then the sides of opposite those angles are?

Corollary 1
congruent

C1 - an equiangular triangle is also equilateral
Theorem 4-3: AAS Theorem: if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are
congruent
Theorem 4-4: HL Theorem: If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are
congruent
Summarize the ways triangles can be proved to be congruent

All triangles (4 ways)
Right Triangles only
All Triangles: SSS SAS ASA AAS

Right Triangle: HL
Definition: Perpendicular Bisector
in a given plane there is exactly one line perpendicular to asegment at its midpoint
Theorem 4-5: If a point lies on the perpendicular bisector of a segment, then
the point is equidistant from the endpoints of the segments
Theorem 4-6: If a point is equidistant from the endpoints of a segment, then the point lies
on the perpendicular bisector of the segment
Definition: Median of a triangle
a segment from a vertex to the midpoint of the opposite side
Definition: Altitude of a triangle
the perpendicular segment from a vertex to the line that contains the opposite side
In a right Triangle describe two 'altitudes'
1 - either leg of the triangle

2 - the third altitude is the inside the triangle
In an obtuse triangle how many altitudes are 1) outside of the triangle and 2) inside the triangle?
2

1
Theorem 4-7: If a point lies on the bisector of an angle, then the point is
equidistant from the sides of the angle
Theorem 4-8: If a point is equidistant from the sides of an angle, then the point
lies on the bisector of the angle
Every triangle has how many Altitudes? How many Medians?
3 and 3
Theorem 5-1: Opposite sides of a parallelogram are
congruent
Theorem 5-2: Opposite angles of a parallelogram
congruent
Theorem 5-3: Diagonals of a parallelogram
bisect each other
Theorem 5-4: If both pairs of opposite sides of a quadrilateral are congruent, then the
quadrilateral is a parallelogram
Theorem 5-5: If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the
quadrilateral is a parallelogram
Theorem 5-6: If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram
Theorem 5-7: If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram
Name 5 ways to prove that a quadrilateral is a parallelogram
1 - show that both pairs of opposite sides are parallel
2 - show that both pairs of opposite sides are congruent
3- Show that one pair of opposite sides are both congruent and parallel
4 - show that both pairs of opposite angles are congruent
5 - show that the diagonals bisect each other
Theorem 5-8: If two lines are parallel, then all points on one line are
equidistant from the other line
Theorem 5-9: If three parallel lines cut off congruent segments on one transversal, then they
cut off congruent segments on every transversal
Theorem 5-10: A line that contains the midpoint of one side of a triangle and is parallel to another side passes
through the midpoint of the third side
Theroem 5-11: Two Parts
The segment that joins the midpoints of two sides of a triangle;
1) is parallel to

2) is half as long
1) the third side

2) as the third
Theorem 5-12: The diagonals of a rectangle are
congruent
Theorem 5-13: The diagonals of a rhombus are
perpendicular
Theorem 5-14: Each diagonal of a rhombus bisects
two angles of the rhombus
Theorem 5-15: The midpoint of the hypotenuse of a right triangle is equidistant
from the three vertices
Theorem 5-16: If an angle of a parallelogram is a right angle then the parallelogram is a
rectangle
Theorem 5-17: If two consecutive sides of a parallelogram are congruent, then the parallelogram is a
rhombus
Theorem 5-18: Base angles of an isosceles trapezoid are
congruent
Theorem 5-19: The Median of a trapazoid is

1) is parallel to

2) has a lenght equal to the
1) the bases

2) average of the bases lenghts
Theorem 6-1: The measure of an exterior angle of a triangle is greater than
the measure of either remote interior angle
Properties of Inequality (5)
if a>b and c>=d, then a+c>b+d

if a>b and c>0, then ac>bc and a/c>b/c

if a>b and c<0, then ac<bc and a/c<b/c

if a>b and b>c, then a>c

if a=b+c and c>0, then a>b
Of the following If-Then Statement "if p, then q", state the;

1) Converse statement

2) Inverse statement

3) Contrapositive statement
1) if q, then p

2) if not p, then not q

3) if not q, then not p
Indirect Proof Steps (3)
1) assume a conclusion is not true (temporarily)

2) reason until you reach a contradiction of a known fact

3) point out the temporary assumption was false and that the conclusion is true
Theorem 6-2: If one side of a triangle is larger than a second side, then the angle opposite the first side is larger than the
angle of the second side
Theorem 6-3: If one angle of a triangle is larger than a second angle, then the side opposite the first angle is...

Corollary 1, 2
longer than the side opposite the second angle

C1 - the perpendicular segment from a point to a line is the shortest segment from the point to the line

C2 - the perpendicular segment from a point to a plane is the shortest segment from the point to the plane
Theorem 6-4:
The Triangle Inequality Theorem:
The sum of the lenghts of any two sides of a triangle is greater than
the lenght of the third side.
Theorem 6-5:
SAS Inequality Theorem:
If two sides of one triangle are congruent with two sides of another triangle, but the included angle of the first is larger than the second, then the third side of the first triangle is
larger than the second Triangle
Theorem 6-6:
SSS Inequality Theorem:
If two sides of triangle are congruent but the third side of one is longer, then the include angle of the first triangle is
larger than the second triangle
Definition: Ratio
one number divided by the other - usually in it's simplest form
Definition: Proportion
when two ratios are equal
Properties of Proportions:

a:b = c:d

what are the means?
what are the extremes?
b,c

a,d
In proportions, what are the products of the means and extremes equal to?
one another
Polygons are Similar if their vertices can be paired such that ? (2 conditions)
1 - corresponding angles are congruent

2 - corresponding sides are in proportion
Postulate 15:
AA Similarity Postulate
if two angles of one triangle are congruent to two angles of the second triangle then the triangles are Similar
Theorem 7-1
SAS Similarity Theorem:
If one angle of two triangles are congruent and the sides including those angles are proportional, then the triangles are
similar
Theorem 7-2:
SSS Similarity Theorem:
If the sides of two triangles are in proportion, then
the triangles are similar
Theorem 7-3:
Triangle Proportionality Theorem:
If a line parallel to one side of a triangle intersects the other, then

Corollary 1
it divides those sides proportionally

C1 - if three parallel lines intersect two tranversals, then they divide the tranversal proportinoally
Theorem 7-4:
Triangle Angle-Bisector Theorem:
If a ray bisects an angle of a triangle, then
it divides the opposite side into segments proportional to the other two sides
Theorem 8-1:
If the altitude is drawn to the hypotenuse of a right triangle, then

Corollary 1, 2
the two triangles formed are similar to the the original triangle, and to each other

C1 - When the altitude is drawn to the hypotenuse of a right triangle, the lenght of the altitude is the geometric mean between the segments of the hypotenuse

C2 - when the altitude is drawn to the Hypot. of a right triangle, each leg os the geometric 'mean' between the hypot. and the segment of the hypot that is adjacent to that leg.
Theorem 8-2:
Pythagorean Theorem: In a right triangle, the square of the Hypot is equal to the
square of the sum of the legs
Theorem 8-3:
If the square of one side of a triangle is equal the sum of the squares of the other two sides, then the
triangle is a right triangle
Theorem 8-3: If
c^2 = a^2 + b^2, then the triangle is
right
Theorem 8-4: if
c^2 < a^2 + b^2, then the triangle is
acute
Theorem 8-5: if
c^2 > a^2 + b^2, then the triangle is
obtuse
Theorem 8-6: 45-45-90 Theorem: In a 45-45-90 triangle, the hypotenuse is
square root of 2 times as long as a leg
Theorem 8-7: 30-60-90 Theorem: In a 30-60-90 triangle the hypot. is
- twice as long as the shorter leg

- the longer leg is the square root of 3 times as long as the shorter leg
Tangent Ratio of Angle A is
Opposite / Adjacent
Sine Ratio of Angle A is
Opposite / Hypotenuse
Cosine Ratio of Angle A is
Adjacent / Hypotenuse
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB + BC = AC