Geometry Definitions

Truth value

True or False

Closed statements

closed statements have truth values

Open statements

open statements could be true or false

logically equivalent

logically equivalent statements have the same truth values

Negation

changes truth falue from true to false, or false to true

conditional statements

if p then q statements

converse

reverses (pthenq) into (qthenp)

inverse

negates hypothesis and conclusion (pthenq) into (not p then not q)

biconditional

combines original with converse (if p then q and if q then p) or (p if and only if q)

contrapositive

converse+inverse (not q then not p)

concurrent lines

lines that meet at a single point

working line

a line you draw to start a construction

isosceles

triangle with at least 2 congruent sides, legs always congruent

equilateral

all sides are equal

altitude

cevian from vertex and perpendicular to the opposite side or extension of the opposite side

median

cevian from vertex to the midpoint of opposite side

perpendicular bisector

line perpendicular to a segment through the midpoint of the segment

angle bisector

Congruent adjacent angles are angle bisectors

orthocenter

altitudes

centroid

medians

circumcenter

perpendicular bisectors

incenter

angle bisectors

auxiliary line

a line introduced in a diagram

inscribe a circle about a triangle

fit the largest circle in a triangle where it touches each side once

circumscribe a circle about a triangle

wrap a triangle with a circle through each vertex