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Geometry chapter 1
Chapter 1 only
Term | Definition |
---|---|
point | a specific location |
line | a connected straight path |
plane | a flat surface |
line segment | a portion of a line consisting of two points and all points between them |
ray | a portion of a line that starts at a point and continues forever in a direction |
parallel | lines that lie in the same plane but do not intersect |
coplanar | points that lie in the same plane |
colinear | points the lie on the same line |
postulate | a statement that is accepted true without proof |
segment addition postulate | AB+BC=AC |
distance formula | (x2-x1)2+(y2-y1)2 |
midpoint | the point that divides the segment into two segments that have the same length |
segment bisector | A line, ray, or other figure that passes through the midpoint of a segment |
midpoint formula | (x1+x2, y1+y2) 2 2 |
angle | a figure formed by two rays with the same endpoint |
vertex | the common endpoint |
degrees | A common measurement unit for circular arcs |
acute angle | 0<m<A<90 |
right angle | m<A=90 |
obtuse angle | 90<m<A<180 |
angle bisector | a ray that divides an angle into two angles that both have the same measure |
Angle Addition Postulate | m<PQR=m<PQS+m<SQR |
Transformation | a function that changes the position, shape, and/or size of a figure |
Image | the output |
Preimage | a figure that is used as the input of a transformation |
Rigid motion | a transformation that changes the position of a figure without changing the size or shape of the figure |
Conjecture | a statement that is believed to be true |
Inductive reasoning | the process of reasoning that a rule or statement may be true by looking at the specific cases |
Deductive reasoning | the process of using logic to prove whether all cases are true |
Theorem | a statement that you can prove is true using a series of logical steps |
Counterexample | an example that shows a conjecture to be false |
Addition Property of Equality | a=b, then a+c=b+c |
Subtraction Property of Equality | a=b, then a-c=b-c |
Multiplication Property of Equality | a=b, then ac=bc |
Division Property of Equality | a=b, then c does not equal 0, then a/c=b/c |
Reflexive Property of Equality | a=a |
Symmetric Property of Equality | a=b, then b=a |
Transitive Property of Equality | a=b, then b=c, then a=c |
Substitution Property of Equality | a=b, then b can be substituted for a in any expression |
Linear Pair Theorem | a pair of adjacent angles whose non-common sides are opposite rays |