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# Geometry Vocabulary

### Theorems, axioms, postulates, properties in Geometry

TermDefinition
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
Created by: thsndbkwrms