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point
a location which has not size. represented by a dot.
line
a straight path that has no thickness and extends forever
plane
a flat surface that has no thickness and extends forever
Collinear Points
Point that lie on the same line.
Coplanar Points
points that lie in the same plane.
Segment
is the part of a line consisting of two points, and all points between them.
Endpoint
A point at either end of a line segment, or a point at one end of a ray.
Ray
A part of a line, with one endpoint, that continues without end in one direction
Opposite rays
two rays that share the same endpoint and form a line
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Midpoint Definition
A point that divides a segment into two congruent segments
Bisects Definition
divides in two equal parts
Acute Angles
angles that are less than 90 degrees
Right Angles
angles that measure 90 degrees
Obtuse Angles
angles that measure above 90 degrees
Straight Angles
two rays that create an angle that measures exactly 180 degrees and forms a straight line
Angle Addition Postulate
If P is in the interior of <RST, then m<RSP + m<PST = m<RST
Angle Bisector
a ray that divides an angle into two congruent angles
Adjacent Angles
two angles in the same plane with a common vertex and a common side, but no common interior points
Linear Pair
A pair of adjacent angles whose noncommon sides are opposite rays.
Supplementary Angles
Two angles whose sum is 180 degrees
Complementary Angles
two angles whose measures have a sum of 90 degrees
Rectangle Perimeter and Area formula
P=2l+2w
A=lw
Square Perimeter and Area Formula
P=4s
A=s^2
Triangle Area and Perimeter Formula
A= 1/2 bh and A= s1+s2+s3.
Circumference and area of a circle
Circumference: PI * 2 * r
Area: PI * r ^2
Midpoint Formula
(x₁+x₂)/2, (y₁+y₂)/2
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Pythagorean Theorum
a²+b²=c²
Reflection
A transformation that "flips" a figure over a mirror or reflection line.
Rotation(transformations)
CIRCULAR MOVEMENT AROUND AN AXIS
Translation
A transformation in which all points of a figure move the same distance in the same direction.
Inductive Reasoning
A type of logic in which generalizations are based on a large number of specific observations.
conjecture
an opinion or conclusion formed on the basis of incomplete information
Counter example
an example that shows a conjecture is false
Conditional Statements
a statement that can be written in if-then form
Hypothesis of conditional statement
the "if" part of a conditional statement
Conclusion of conditional statement
the "then" part of a conditional statement
Truth Value
the truth or falsity of a statement
Converse
If q, then p
Inverse
If not p, then not q
Contrapositive
If not q, then not p
logically equivalent statements
related conditional statements that have the same truth value
Deductive Reasoning
reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)
Law of Detachment
If p --> q is a true statement and p is true, then q is true
Law of Syllogism
when p->q is true, and q->r is true, then p->r is true
Biconditional Statements
a statement that can be written in the form "p if and only if q"
Addition Property of Equality
If a=b, then a+c=b+c
Subtraction POE
If a=b, then a-c=b-c
Multiplication POE
If a=b, then ac=bc
Division POE
If a = b and c ≠ 0, then a/c = b/c
Reflexive POE
a=a
Symmetric POE
if a=b, then b=a
Transitive POE
If a=b and b=c, then a=c
Substitution POE
If a=b, then b can be substituted for a in any expression
Reflexive POC
AB is congruent to AB
Symmetric POC
if <A is congruent to <B, then <B is congruent to <A
Transitive POC
if <A ≅ <B and <B ≅ <C, then <A ≅ <C
Linear Pair Thrm
If two angles for a linear pair, then supplementary
Congruent Supplements Theorem
If two angles are supplementary to the same angle, then they are congruent
Right Angle Congruence Thrm
All right angles are congruent
Congruent Complements Thrm
if two angles are complementary to the same angle ( or to congruent angles) then they are congruent
Common Segments Theorem
If AB is congruent to CD, then AC is congruent to BD
Vertical Angle Theorem
Vertical angles are congruent
Parallel Lines
lines in the same plane that never intersect
Perpendicular Lines
Two lines that intersect to form right angles (90 degrees)
Skew Lines
Lines that do not intersect and are not coplanar
Parallel Planes
two planes that do not intersect
Transversal
a line that intersects two or more coplanar lines at different points
Correspodning Angles
The pairs of angles formed on the same side of the transversal and in the same relative position
Alternate Interior Angles
angles between 2 lines and on opposite sides of a transversal
Alternate Exterior Angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
Same-side Interior Angles
two interior angles on the same side of the transversal
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Alternate Interior Angle Theorum
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Alternate Exterior Angle Theorum
If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
Same-side Interior Angle Theorem
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
Converse of Alternate Interior Angle Theorem
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel
Converse of Alternate Exterior Angle Theorem
If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.
Converse of the Same-Side Interior Angles Theorem
If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel.
perpendicular bisector
A line that is perpendicular to a segment at its midpoint.
Slope Formula
m=y2-y1/x2-x1
Point Slope Formula
y-y₁=m(x-x₁)
Slope Intercept Form
y=mx+b
equation of a vertical line
x=a, where a is the x-intercept
equation of a horizontal line
y=b, where b is the y-intercept
Parallel Lines
Have the same slope, but different y-intercept
Intersecting Lines
Different Slopes
coinciding lines
same slope, same y-intercept
Acute Triangle
A triangle with 3 acute angles
Right Triangle
A triangle that has a 90 degree angle.
Obtuse Triangle
A triangle with one angle that is greater than 90 degrees.
Equiangular Triangle
A triangle with 3 congruent angles
