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Geometry
| Question | Answer |
|---|---|
| Chapter 1 | :) |
| conjecture | is an unproven statement that is based on observations |
| inductive reasoning | looking for patterns and making conjectures |
| counterexample | an example that shows a conjecture is false |
| point | has no dimension usually represented as a small dot |
| line | extends in one dimension and extends without end. (represented as a straight line with 2 arrowheads.) |
| plane | extends in 2 dimensions. planes also extends without end. |
| collinear points | points that lie on the same line |
| coplanar points | points that lie on the same plane |
| distance formula | √((x₂ - x₁)² + (y₂ - y₁)²) |
| congruent segments | segments that have the same length |
| Ruler's Postulate | The points on a line can be matched one to one with real numbers. The real number that matches to a point is the coordinate of the point. The postulate finds the distance between 2 points on a line with d = |C₁ - C₂| |
| Segment Addition postulate | if a point lies on a line segment, the lengths of the two smaller segments formed by that point will add up to the length of the original, larger segment: Ex: AB + BC = AC then B is between A and C |
| ANGLE | FORMED BY TWO RAYS WITH THE SAME ENDPOINT CALLED A VERTEX |
| VERTEX | END POINT SHARED BY TWO RAYS |
| Angle congruence | angles that have the same measure |
| Angle Addition postulate | if a ray divides an angle into two smaller, adjacent angles, the sum of the measures of the two smaller angles equals the measure of the larger, original angle. |
| acute | less than 90 degrees |
| obtuse | more than 90 degrees |
| right angle | 90 degrees |
| straight angle | 180 degrees |
| adjacent angles | share a common vertex or side but have no common interior points |
| midpoint | point that bisects the segment into 2 congruent segments |
| bisects | divides |
| segment bisector | a segment, line, ray, or plane that bisects a segment. |
| Midpoint formula | 𝑥1 + 𝑥2/2, y1 + y2/2, |
| vertical angles | angle sides form 2 pairs of opposite rays |
| linear pair | noncommon sides are opposite rays |
| Chapter 2 | :) |
| conditional statement | has 2 parts a hypothesis and a conclusion |
| if-then form | when a statement has a hypothesis (the if) and a conclusion (then) |
| Postulate 5 | Through any 2 points there exists exactly one line |
| Postulate 6 | a line contains at least two points |
| Postulate 7 | If two planes intersect, then their intersection is a line. |
| Postulate 8 | Through any 3 noncollinear points, there exists exactly 1 plane. |
| Postulate 9 | A plane contains at least 3 noncollinear points |
| Postulate 10 | if 2 points lie on a plane, then the line containing them lies in the plane. |
| Postulate 11 | if 2 planes intersect, then their intersection is a line. |
| converse | opposite of if then form (then if form) |
| inverse | when you negate the statement |
| contrapositive | the result of a inverse statement |
| equivalent statements | when 2 statements are both true or false |
| perpendicular lines | if they intersect to form right angles |
| biconditional statement | a statement that contains "if and only if" |
| Addition Property of Equality | If (a=b), then (a+c=b+c) |
| Subtraction Property of Equality | If (a=b), then (a-c=b-c) |
| Multiplication Property of Equality | If (a=b), then (ac=bc) |
| Division Property of Equality | If (a=b) and c is not equal to 0, then a/c = b/c |
| Relational properties Reflexive Property | For any number (a), (a=a) |
| Symmetric Property | If (a=b), then (b=a) |
| Transitive Property | If (a=b) and (b=c), then (a=c) |
| Substitution Property | If (a=b), then (a) may be substituted for (b) (or vice versa) in any equation or expression |
Created by:
chaotic_devil>:)