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Geometry Final Cheat Sheet by

Cheat sheet for my Geometry Final

Vocabulary

Segment
Part of a line consisting of two end points and the points between them
Ray
Part of a line consisting of an end point and all the points to one side
Opposite rays
2 collinear rays with the same endpoint; forms a line
Parallel Lines
Coplaner lines that do not intersect
Skew Lines
Non-co­planer lines that do not intersect
Parallel Planes
Planes that do not intersect
Congruent Segments
2 segments with the same length
Midpoint
Point on a segment that divides a segment into 2 congruent segments
Angle
Formed by two rays with the same endpoint.
Acute Angle
Angle Greater than 0 and less than 90
Right angle
90 degree angle
Obtuse angle
Angle greater than 90 but less than 180
Straight Angle
180 degree angle
Congruent angles
Angles with the same measure
Vertical angles
Opposite angles formed by inters­ecting lines
Adjecent angles
2 coplaner angles that share a common vertex and a common side
Comple­mentary angles
2 angles that add up to 90 degrees
Supple­mentry angles
2 angles that add up to 180 degrees
Condit­ional
An if/then statement
Hypothesis
What follows the If in a condit­ional
Conclusion
What follows the then in a condit­ional
Truth Value
If a condit­ional is true or false
Converse
Palendrome of a condit­ional
Bicond­itional
The combin­ation of a condit­ional statement and its converse
Deductive Reason­ing­/Lo­gical Thinking
The process of reasoning from a given statement to a conclusion
Negation
Opposite of the truth value
Inverse
Negates both the hypothesis and the conclusion
Contra­pos­otove
Switches the hypothesis and the conclusion and negates both
Transv­ersal
A line that intersects 2 or more coplaner lines at distinct points
Equian­gular Triangle
All angles are congruent
Acute Tringle
all angles are acute
Right Triangle
one right angle
Obtuse Triangle
one obtuse angle
Equala­teral Triangle
All sides are congruent
Isosceles Triangle
2 congruent sides
Scalene Triangle
No congruent sides
Exterior angle
Angle formed by a side and an extention of an adjacent side
Polygon
A closed plane figure with at least 3 sides that are segments. The sides only intersect at end points, no adjacent sides are congruent
Convex Polygons
No "­den­ts"
Concave polygon
Has a "­den­t" or "­den­ts"
Equila­teral Polygon
a polygon where all sides are congruent
Equian­gular polygon
a polygon where all angles are congruent
regular polygon
a polygon that is both equian­gular and equala­teral
Congruent Polygons
Polygons with congruent corres­ponding sides and angles
Corollary
a statement that follows directly from a theorem
Midsegment
a segment that connects the midpoints of 2 sides of a triangle
Perpen­dicular Bisector
a line segment or ray that is perpen­dicular to a segment through its midpoint
Concurrent
When 3 or more lines intersect in one point
Point of concur­rency
Point where 3 concurrent lines intersect
Circum­center
The point of concur­rency of the perpen­dicular bisectors of a triangle
circum­scribed circle
circle that passes through all the vertices of a triangle
Obtuse Circum­center
Lies outside the triangle
Right Circum­center
midpoint of the hypotenuse
Acute circum­center
Lies within the triangle
Angle Bisector
Ray that divides an angle into to congruent segments
Incenter
Point of concur­rency of the angle bisectors of a triangle
Inscribed Circle
Largest circle contained in a triangle that touches all three sides
Median
Segment whose endpoints are a vertex and the midpoint of the opposite side
centroid
point of concur­rency of the medians; always lies within the triangle
Altitude
Height of a triangle
Quadri­lateral
Polygon with 4 sides
Parall­elogram
A quadri­lateral with 2 pairs of opposite parallel sides
Rhombus
Quadri­lateral with all sides congruent and 2 pairs of opposite parallel sides
Rectangle
Parall­elogram with four right angles
Square
A parall­elogram with four congruent sides and four right angles
Kite
Quadri­lateral with two pairs of adjacent sides congruent and no opposite sides congruent
Trapezoid
A quadri­lateral with exaclty one pair of parallel sides
Isosceles Trapezoid
A trapezoid whose non-pa­rallel sides are congruent
Consec­utive Angles
Angles of a polygon that share a side; are supple­mentary
Base angles
two angles that share a base of a trapezoid
Proportion
a statement that 2 ratios are equal
Indirect Measur­ement
Used to find the lengths of objects that are too difficult to measure directly
Vector
any quantity with magnitude (size) and direction
Magnitude
Distance from initial point to terminal point
Tangent line to a circle
A line on the same plane as a circle that intersects the circle at exactly one point
point of tangency
point where a circle and tangent line intersect
Apothem
Perpen­dicular distance from the center of a regular polygon
Circle
The set of all points in a plane equidi­stant to a given point called the center
radius
a segment w/ one endpoint at the center and the other in the circle
Diameter
a segment that contains the center and has both endpoints on a circle
Congruent circles
circles with congruent radii or diameters
central angle
an angle whose vertex is the center of the circle
Arc
Part of circle
Semi-c­ircle
Half a circle
Minor Arc
Smaller than a semi-c­ircle
Major arc
Greater than a semi circle
adjacent arc
arcs of the same circle that have exactly one point in common
Circum­ference
Perimeter of a circle
concentric circles
coplanar circles that share a center

All the other crap continued

Theorem 12-1
If a line is tangent to a circle, then the line is perpen­dicular to the radius drawn to the point of tangency
Theorem 12-2
If a line is in the plane of a circle is a radius at its endpoint on the circle, then the line is tangent to the circle
Theorem 12-3
The two segments tangent to a circle from a point outside the circle are congruent
Perimiter of a Square
4S
Area of a Square
S2
Perimiter of a Rectan­gle­/Pa­ral­lel­ogram
2B+2H
Area of a Rectan­gle­/Pa­ral­lel­ogram
BH
Circum­ference
PiD or 2PiR
Area of a Circle
PiR2
Perimiter of a Triangle
S1+S2+S3
Area of a Triangle
.5(b*h)
Area of a Trapezoid
.5(b1*b2)h
Area of a Rhombu­s/Kite
.5(d1*d2)
Area of Regular Polygons
.5AP
Arc Addition Postulate
The whole is equal to the sum of its parts
Arc Length
 

Postul­ates, Formulas, etc...

Ruler Postulate
The points of a line can be put into 1:1 corres­pon­dence with the real numbers AB=|A-B|
Segment addition postulate
If three points (A,B,C) are colliner and B is between A and C, then AB+BC=AC; The whole is equal to te sum of its parts
Vertical Angles Theorem
Vertical angles are congruent
Law of detachment
If P->Q and P is true, then Q is true
Law of syllogism
If P->Q and Q->R are true, then P->R is true
Addition Property
A=B, then A+C=B+C
Subtra­ction Property
A=B, then A-C=B-C
Multip­lic­ation Property
A=B, then AC=BC
Division Property
A=B and C is not 0, then (A/C)=­(B/C)
Reflexive Property
A=A
Symmetric Property
A=B and B=A
Transitive Property
A=B and B=C, then A=C
Substi­tution Property
A=B, so B can replace A in equations
Distri­butive property
A(B+C)= AB+AC
Congruent Supple­ments Theorem
If 2 ngles are supple­ments of the same angle or of congruent angles, then that angles are congruent
Congruent Comple­ments Theorem
If 2 angles are comple­ments of the same angle or of congruent angles, then the 2 angles are congruent
Right Angle Congruence
All right angles are congruent
Corres­ponding angles are congruent
Implys parallel lines
Alternate Interior angles are congruent
Implys parallel lines
Same side Interior angles are supple­mentry
Implys parallel lines
Alternate exterior angles are congruent
Implys parallel lines
Same side Exterior angles are supple­mentry
Implys parallel lines
If two lines are parallel to the same line
Then they are Parallel
If 2 coplaner lines are perpen­dicular to the same line
then they are parallel
Sum of a triangle's angle measures
180 degrees
Triangle exterior angle Theorem
The measure of each exterior angle of a triangle equals the sum of it's two remote exterior angles
Degrees in a Quadri­lateral
360
Degrees on a Pentagon
540
Degrees in a hexagon
720
Degrees in a octagon
1080
Theorem 4-1
If two angles of one triangle are congruent to two angles of another triangle, then they are congruent
CPCTC
Corres­ponding Parts of Congruent Triangles are congruent
SSS; Side Side Side
If 3 sides of a triangle are congruent to 3 sides of another triangle, then they are congruent
SAS; Side Angle Side
If 2 sides and 1 included angle of a triangle are congruent to the 2 sides and angle of another triangle, then they are congruent
ASA; Angle Side Angle
If 2 angles and an included side of a triangle are congruent to 2 angles and included side of another triangle, then they are congruent
AAS; Angle Angle Side
If 2 angles and a non-in­cluded side of a triangle are congruent to 2 angles and non-in­cluded side of another triangle, then they are congruent
Isosceles Triangle Theorem
If the 2 sides of a triangle are congruent, then the base angles are congruent
Converse Isosceles Triangle Theorem
If the 2 base angles of a triangle are congruent, then the sides are congruent
HL; Hypotenuse Leg
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then they are congruent
Triangle Midsegment theorem
If a segment joins the midpoints if 2 sides of a triangle, then the segment is parallel to the third side and is half the length
Perpen­dicular Bisector theorem
If a point is on the perpen­dicular bisector of a segment, then it is equidi­stant from the endpoints of the segment
Converse of the Perpen­dicular Bisector theorem
If a point is equidi­stant from the endpoints of a segment, then it is on the perpen­dicular bisector of the segment
Angle Bisector theorem
If a point is on the angle bisector of an angle, then the point is wquidi­stant to the sides of the angle
the converse of the Angle Bisector theorem
If a point in the interior of an angle is equidi­stant to the sides of the angle, then the point is on the angle bisector
Theorem 5-6
The perpen­dicular bisectors of the sides of a triangle are concurrent at a point equidi­stant from the vertices
Theorem 5-7
The Bisectors of the angles of a triangle are concurrent at a point equidi­stant from the sides
Theorem 5-8
The mediams of a triangle are concurrent at a point that is two thirds the distnce from each vertex to the mid point of the opposite side
Theorem 5-9
The Lines that contain the altitudes of a triangle are concurrent
Comparison Property
If A=B+C and C>0, then A>B
Distance formula
Midpoint Formula
Slope Intercept Form
Y=Mx+B
Standard Form
Ax+By=C
Point Slope Form
Y-Y1=M(X-X1)
Theorem 6-1
Opposite sides of a parall­elogram are congruent
Theorem 6-2
Opposite angles of a parall­elogram are congruent
Theorem 6-3
The diagonals of a parall­elogram bisect each other
Theorem 6-4
If three or more parallel lines cut off congruent segments on one transv­ersal, then they cut off congruent segments on every transv­ersal
Theorem 6-5
If both pairs of opposite sides of a quadri­lateral are congruent, then the quadri­lateral is a parall­elogram
Theorem 6-6
If both pairs of opposite angles of a quadri­lateral are congruent, then the quadri­lateral is a parall­elogram
Theorem 6-7
If the diagonals of a quadri­lateral bisect each other then the quadri­lateral is a parall­elogram
Theorem 6-8
if one pair of opposite sides of a quadri­lateral are both parallel and congruent, then the quadri­lateral is a parall­elogram
Theorem 6-9
Each diagonal of a rhombus bisects 2 angles of the rhombus
Theorem 6-10
The diagonals of a rhombus are perpen­dicular
Theorem 6-11
The Diagonals of a rectangle are congruent
Theorem 6-12
If one diagonal of a parall­elogram bisects 2 angles of the parall­elo­gram, then it is a rhombus
Theorem 6-13
If the diagonals of a parall­elogram are perpen­dic­ular, then it is a rhombus
Theorem 6-14
If the diagonals of a parall­elogram are congruent, then the parall­elogram is a rectangle
Theorem 6-15
The Base angles of an isosceles trapezoid are congruent
theorem 6-16
Diagonals of an isosceles trapezoid are congruent
AA~; angle angle similarity
If 2 angles of one triangle are congruent to 2 angles of another triangle, then they are similar
SAS~; Side Angle Side similarity
If an angle of one triangle is congruent to an angle of an angle of a second triangle, and the sides surrou­nding the angle are propot­ional, then they are similar
SSS~; Side Side Side similarity
If the corres­ponding sides of two triangles are propor­tional, then they are similar
Theorem 7-3
The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles that are similar to the original and eachother
Corollary 1 to Theorem 7-3
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse
Corollary 2 to Theorem 7-3
The altitude of the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse
Side-S­plitter Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then its divides those sides propor­tio­nally
Corollary to Side-S­plitter
If three parallel lines intersect 2 transv­ersals, then the segments interc­epted on the transv­ersals are propor­tional
Theorem 7-5
If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are propor­tional to the other two sides of the triangle
Pythag­orean Theorem
A2+B2=C2
Pythagoren Triples
{3,4,5} {5,12,13} {8,15,17} {7,24,25}
C2=A2+B2
Right Triangle
C2>A2+B2
Obtuse Triangle
C2<A2+B2
Acute Triangle
45-45-90 Triangle
In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is square root of 2 times the length of a leg
30-60-90 Triangle
The Hypotenuse is double the length of the shortest leg and the length of the longer leg is square root of 3 times the length of the shorter leg
Tangent
Opposi­te/­Adj­acent
Sine
Opposi­te/­Hyp­otenuse
Cosine
Adjace­nt/­Hyp­otenuse
SohCahToa
You know what this means, dummy
   
 

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  • Published: 4th June, 2016
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