# Geometry definitions, axioms, and theorems

## Terms

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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