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Geometry Vocabulary
Theorems, axioms, postulates, properties in Geometry
| Term | Definition |
|---|---|
| Complementary angles | Two angles whose measures have a sum of 90o |
| Supplementary angles | Two angles whose measures have a sum of 180o |
| Theorem | A statement that can be proven |
| Vertical Angles | Two angles formed by intersecting lines and facing in the opposite direction |
| Transversal | A line that intersects two lines in the same plane at different points |
| Corresponding angles | Pairs of angles formed by two lines and a transversal that make an F pattern |
| Same-side interior angles | Pairs of angles formed by two lines and a transversal that make a C pattern |
| Alternate interior angles | Pairs of angles formed by two lines and a transversal that make a Z pattern |
| Congruent triangles | Triangles in which corresponding parts (sides and angles) are equal in measure |
| Similar triangles | Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) |
| Angle bisector | A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure |
| Segment bisector | A ray, line or segment that divides a segment into two parts of equal measure |
| Legs of an isosceles triangle | The sides of equal measure in an isosceles triangle |
| Base of an isosceles triangle | The third side of an isosceles triangle |
| Equiangular | Having angles that are all equal in measure |
| Perpendicular bisector | A line that bisects a segment and is perpendicular to it |
| Altitude | A segment from a vertex of a triangle perpendicular to the line containing the opposite side |
| Reflexive Property | A quantity is equal to itself |
| Symmetric Property | If A = B, then B = A |
| Transitive Property | If A = B and B = C, then A = C |
| Addition Property of Equality | If A = B, then A + C = B + C |
| Angle Addition Postulate | If a point lies on the interior of an angle, that angle is the sum of two smaller angles with legs that go through the given point |
| Corresponding Angles Postulate | If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent |
| Parallel Postulate | Given a line and a point not on that line, there exists a unique line through the point parallel to the given line |
| Alternate Exterior Angles Theorem | If a transversal intersects two parallel lines, then the alternate exterior angles are congruent. Converse: If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel |
| Alternate Interior Angles Theorem | If a transversal intersects two parallel lines, then the alternate interior angles are congruent. Converse: If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel |
| Congruent Complements Theorem | If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent |
| Congruent Supplements Theorem | If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent |
| Right Angles Theorem | All right angles are congruent |
| Same-Side Interior Angles Theorem | If a transversal intersects two parallel lines, then the interior angles on the same side are supplementary. Converse: If a transversal intersects two lines and the interior angles on the same side are supplementary, then the lines are parallel. |
| Vertical Angles Theorem | If two angles are vertical angles, then they have equal measures |
| Vertical Angles | the angles opposite each other when two lines cross |
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