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# Geometry definitions, axioms, and theorems

## Terms

undefined, object
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Bisector
A line or line segment that goes through the midpoint of another line segment
Collinear Points
Points on the same line
Addition Axiom
If a=b and c=d then a+c=b+d
Division Axiom
If a=b and c≠0 then a/c=b/c
Complementary Angles
Two angles whose measurements add up to 90°
Subtraction Axiom
If a=b and c=d the a-c=b-d
Theorem 3
If 2 angles are supplementary to ≅ ∠'s then they are ≅ to each other
Vertical Angles
Formed by two intersecting lines
Coplanar Points
Points on the same plane
Transitive Axiom
If a=b and b=c then a=c
Linear Pairs
a) adjacent angles b) their non-common side forms a line
Supplementary Angles
Two angles whose measurements add up to 180°
Theorem
A statement that can be proved
Obtuse Angle
Angles measures over 90° but less than 180°
Congruent Segments
Segments that have the same length
Right Angle
Angles that measures at 90°
Angle Bisector
A ray that divides the angle into two ≅ parts
Line
An infinite collection of points-has a length, but no width (a line may be named by 2 points)
Acute Angle
Angles measured at less than 90°
Theorem 1
If 2 ∠'s are supplementary to the same ∠ then they are ≅ to each other
Substitution Axiom
If a=b then b can replace a in any expression and b can replace a in any expression
Point
A location, has no dimensions, represented by a dot, and named by a capital letter
Line Segment
Part of a line consisting of 2 points (endpoints) and all the points on the line in between
Adjacent Angles
a) have a common vertex b) have a common side c) have no common interior points
Plane
An infinite flat surface
Axiom
An angle has one and only one angle bisector
Symmetric Axiom
a=b then b=a
Ray
Part of a line consisting of one endpoint and all the points of the line on one side of that point
Multiplication Axiom
If a=b and c=d then ac=bd
Postulate
A statement which is accepted without proof
Theorem 4
If 2 angles are complementary to ≅ ∠'s then they are ≅ to each other
Midpoint
A point that divides a line segment into two ≅ parts
Angle
The union of two rays that have the same endpoint (vertex)
Perpendicular Lines
Lines or part of lines that intersect to form right angles
Theorem 2
If 2 ∠'s are complementary to the same ∠ then they are ≅ to each other
Congruent Angles
Angles that have the same measure
Opposite Rays
a) They have the same endpoint b) Their union forms a line
Reflexive Axiom
a=a
Straight Angle
Angles that measures at 180°
Supplement Axiom
If 2 ∠'s form a linear pair then they are supplementary

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