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2A Geometry & Logic
Geometry Unit 2A: Geometry and Logic Vocabulary
| Term | Definition |
|---|---|
| Point | An exact location with no size only position |
| Line | A 2-dimension figure that is straight, has no width and extends in both directions infinitely |
| Plane | A 2-dimensional figure with a length and width, but no depth and extends infinitely |
| Collinear | Three or more points on the same line |
| Coplanar | Three or more points on the same plane |
| Line Segment | The part of a line that connects two points |
| Ray | The part of a line with a starting point but no end point that goes on infinitely in one direction |
| Angle | A figure formed by two rays that meet at a common end point known as the vertex |
| Vertex | The common end point in a angle |
| Parallel lines | Lines on the same plane that never intersect (touch) |
| Perpendicular lines | Lines that intersect at a right (90°) angle |
| Skew Lines | Lines on different planes that do not intersect |
| Congruent Segments | Segments that have the same length |
| Congruent Angles | Angles that have the same degree measure |
| Intersecting Lines | Two or more lines that cross each other in a plane intersect at a point |
| Intersecting Planes | When two planes intersect, they intersect each other at a line |
| Intersecting Plane and Line | When a line intersects a plane, they intersect at a point |
| Postulate | A statement that is accepted as true without proof |
| Theorem | A statement that has been proven using definitions, properties, postulates, or other theorems |
| Proof | A logical mathematical argument used to show the truth of a mathematical statement |
| Reflective - Property of Equations | a = a |
| Symmetric - Property of Equality | If a = b, then b = a |
| Transitive - Property of Equality | If a = b and b = c, then a = c |
| 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 Equation | If a = b, then a•c = b•c |
| Division - Property of Equation | If a = b and c does not equal zero (0), then a/c = b/c |
| Substitution - Property of Equality | If a = b, then a may be replaced with b (or vice versa) in any equation or expression |
| Distributive - Property | a(b + c) = ab + ac |
| Definition of Congruence | Two figures are congruent if and only if their measures are equal |
| Midpoint | The point in the middle of a segment. The midpoint divides the segments into two congruent (equal to 90) segments |
| Segment Bisector | A ray, line, or segment that divides a segment into 2 congruent (equal to 90) segments |
| Perpendicular Bisector | A ray, line, or segment that divides a segment into 2 congruent (equal to 90) segments and intersects at a right (90°) angle |
| Angle | Is formed by two rays with a common endpoint |
| Vertex | The common endpoint of an angle |
| Sides | The rays of the angle |
| How do you name an angle? | ∠ABC: if using 3 letters, the middle letter must always represent the vertex! |
| How do you name an angle? | ∠B: use a single letter if there is only ONE angle located at the vertex You can use a number (not measure) if a number is provided •When referring to the measure, remember to use a lowercase m before the angle: m∠ABC = 60° |
| Adjacent Angles | Angles that share a side and a vertex but do not overlap |
| Angle Bisector | A ray, line, or segment that divides an angle into 2 congruent angles |
| Linear Pair Property | A pair of adjacent angles formed when 2 lines intersect |
| Complementary Angles | Two angles whose sim is 90° |
| Supplementary Angles | Two angles whose sum is 180° |
| Vertical Angles | The opposite angles formed when two lines intersect. Vertical lines are always congruent |
| Transversal | A line that intersects two or more lines |
| Corresponding Angles | Are on the same side of the transversal and in the same position |
| Alternate Interior Angles | Interior angles, non-adjacent, and on opposite sides of the transersal |
| Alternate Exterior Angles | Exterior angles, non-adjacent, and in opposite sides of the transversal |
| Same Side (Consecutive) Interior Angles | Interior angles that are on the same side of the transversal |
| A LINEAR PAIR is always... | SUPPLEMENTARY |
| Each pair of VERTICAL ANGLES angles are always... | CONGRUENT |
| Each pair of CORRESPONDING ANGLES is... | CONGRUENT |
| Each pair of ALTERNATE INTERIOR ANGLES is... | CONGRUENT |
| Each pair of ALTERNATE EXTERIOR ANGLES is… | CONGRUENT |
| Each pair of SAME SIDE (CONSECUTIVE) INTERIOR ANGLES is... | SUPPLEMENTARY |
| Converse of Corresponding Angles Postulate | If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. |
| Converse of Alternate Interior Angles Theorem | If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel |
| Converse of Alternate Exterior Angles Theorem | If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel |
| Converse of Same Side (Consecutive) Interior Angles Theorem | If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel |
| Acute angle | an angle that measures less than 90 degrees |
| Corresponding sides | Sides that have the same relative positions in geometric figures. |
| Endpoint | A point at one end of a segment or the starting point of a ray. |
| Obtuse angle | An angle that measures more than 90 degrees but less than 180 degrees |
| Right Angle | an angle that measures 90 degrees (°) |
Created by:
taniaph
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