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Geometry Exam Cheat Sheet (DRAFT) by

Geometry formulas,theorems.

This is a draft cheat sheet. It is a work in progress and is not finished yet.

All Formulas

Interior Angles:
Sum of the measures of interior angles of a triangle = 180
Exterior Angle of a Triangle:
m∠1= m∠A+m∠B
Exterior Angles:
Sum of the measure of exterior angles of a convex polygon = 360
Given Point:
A(x1,y1) and B(x2,y2)
Midpoint:
(x1+x2/2, y1+x1/2)
Distance Formula:
Slope
rise/run= y2-y1/­x2-x1
Slope- Intercept form of linear equation with slope m and y-inte­rcept b:
y=mx+b
Zero slope:
Horizontal
Negative slope:
Goes down left to right
Positive slope:
Rises left from to the right
Undefined Slope:
vertical slope of parallel lines: same slope. Slope of perpen­dicular lines: m1. m2=-1 : write an equation from the graph then fin the slope & y value.

Symbols

AB - Line AB
Ab - Segment AB
AB - Ray AB
≅ - Congruent
∠ABC - Angle ABC
m∠A - Measure of angle A
|- Perpen­dicular to
|| - Parallel to
m - Slope
Δ ABC - Triangle ABC
< - Is less than
> - Is greater than
≠- Is not equal to
≅ - Is not congruent to

All Proper­ties:

Addition Property of Equality - A=B then A+C= B+C
Subtra­ction Property of Equality -
Multip­lic­ation Property of Equality -
Devision Property of Equality -
Reflexive Property of Equality - A=A; AB=AB
Reflexive Property of Congruence - AB=(C); CD=AB
Transitive Property of Equality - A=B; B=C; then A=C
Transitive Property of Congruence - A=(C) B B=C; then A=(C) C
Substi­tution Property - If A=B then A can be substi­tuted for B
Distru­butive Property - A(B+C)= AB+AC
Symmetric Property of Equality -If AB=CD, then CD=AB

More Angles

Acute,
Right,
Obtuse
Straight angles
Comple­mentary
Adjacent
Supple­mentary
Medians
Altitudes
Scalene
No congruent sides
Equala­­teral Triangle
All sides are congruent
Isosceles Triangle
2 congruent sides
 

Chapter 3.1

Corres­ponding Angles:
When they have corres­ponding positions
Alternate Interior:
If they lie between the two lines and on opposite sides of the transv­ersal
Alternate Exterior:
If they lie outside the two lines and on opposite sides of the transv­ersal
Consec­utive Interior:
If they lie between the two lines and on the same side of the transv­ersal

All Angle/­Tri­angle Info + Extra Vocab

Acute Angle:
An angle between 0 and 90 degrees.
Acute Triangle:
Triangle with three acute angles
Adjacent Angles:
Altitude of a Triangle
The perpen­dicular segment from one vertex of the triangle to the opposite side/ to the line that contains the opposite side.
Angle:
Has two different rays with the same endpoint. Rays- Sides of the angle. Endpoint- The vertex of the angle.
Angle Bisector:
A ray that divides an angle into two angles that are ≅.
Between:
When 3 points lie on a line, you can say that one point is between the other two
Biocon­dit­ional Statement:
A statement that contains the phrase "if and only if"
Centroid of a Triangle:
The point of concur­rency of the three medians of the triangle.
Circum­fer­ence:
Distance around a circle
Collinear Points:
Points that lie on the same line
Comple­mentary Angles:
Two angles whose measures have the sum 90. The sum of the measures of an angle and its complement is 90.
Condit­ional Statement
A type of logical statement that has two parts- Hypothesis + Conclu­sion... ex: If m∠A=90, then ∠A is a right angle.
Congruency transf­orm­ation/ Isometry
1- Transl­ation. 2- Reflec­tions, 3-Rota­tions
Conjec­ture:
An unproven statement that is based on observ­ati­on... ex: all prime numbers are odd
Contra­pos­itive:
The equivalent statement formed by negating the hypothesis and conclusion of the converse of a condit­ional statement.
Convex Polygon, Concave
A Polygon that is not convex is non-co­nve­x/c­oncave. Convex Polygons = No "­­de­n­t­s", Has a "­­de­n­t­" or "­­de­n­t­s"
Coplanar points
Points that lie in the same plane
Equian­gular Polygon, Equila­ter­al,­pol­ygon, Equila­teral triang­le,­iso­sceles,
Three congruent sides, all of its sides congruent, three congruent sides, at least 2 congruent sides
Heptagon, Hexagon, Pentagon
Polygon with 7 sides, 6 sides, 5 sides,
Hypotenuse
The side of the opposite the right angle.
Skew lines
Lines that don't intersect + are NOT coplanar
 

All Postulates

Ruler "­Pos­tul­ate­" - The points on a line can be matched one to one with the real number­s.The real number number that corres­ponds to a point is the coordinate of the point.
Segment Addition " - If B is between A & C, then AB+BC=AC. If AB+BC=AC then B is between A & C
Protractor " - The measure of ∠AOB is equal to the the absolute value of the difference between the real numbers for OA & OB.
Segment Addition "- If B is between A & C, then AB + BC= AC. If AB+BC=AC, then B is between A & C
Angle Addition " - If P is in the interior of ∠RST, then m∠RST= m∠RSP+ m∠PST.
5 - Through any two point there exists exactly one line
6 - A line contains at least two points
7 -If two lines intersect, then their inters­ection is exactly at one point.
8 - Through any three noncol­linear points there exists exactly one plane
9 - A plane contains at least three noncol­linear points
10 - If two point lie in a plane, then the line containing them lies in the plane
11 -If two planes intersect, then their inters­ection is a line
12 - Linear pair " - If two angles form a linear pair, then they are supple­men­tary.
Corres­ponding Angles Postulate & its Converse- "If two parallel lines are cut by a transv­ers­al", then the pairs of corres­ponding angles are ≅. " " so the corres­ponding angles are ≅, then the lines are ||.
Slopes of Parallel "­Lin­es" - In a coordinate plane two nonver­tical lines are parallel if & only if they have the same slope. Any 2 vertical lines are ||.
Slopes of perpen­dicular " " - In a coordinate plane, two nonver­tical lines are perpen­dicular if and only if the product of their slopes is -1. Horizontal lines are perpen­dicular to vertical lines
SSS "­Con­gruence Postul­ate­" -If 3 sides of a triangle are congruent to 3 sides of another triangle, then they are congruent
SAS " -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 " -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
AA Similarity "-If 2 angles of one triangle are congruent to 2 angles of another triangle, then they are similar
 

All Theorems

Right Angles Congruence "­The­ore­m"-
Congruent Supple­ments "-
Congruent Comple­ments " -
Vertical Angles ≅ "-
Alternate Interior Angles " -
^ Exterior Angles " -
Consec­utive Interior Angles " -
Alternate Interior Angles Converse -
^ Exterior Angles Converse -
Consec­utive Interior Angle Converse -
Transitive Property of Parallel Lines -
Perpen­dicular Transv­ersal-
Lines Perpen­dicular to a Transv­ersal-
Triangle Sum -
Corollary -
Exterior Angle-
Third Angles-
Hypotenuse Leg Congru­ence-
AAS Congru­ence-
Base Angles-
Corollary -
Converse of the Base Angle -
Midsegment -
Perpen­dicular Bisector -
Converse of the Perpen­dicular Bisector -
Angle Bisector -