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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 |