Geometry: Parallel Lines, Angles, Triangles, and Polygons
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41 Terms
parallel lines
lines in the same plane that never intersect
skew lines
lines that do not intersect and are not in the same plane
parallel line and plane
a line and a plane that never intersect
parallel planes
planes that never intersect
perpendicular planes
planes that intersect at a right angle
vertical
straight up and down
horizontal
flat and level
transversal
a line that cuts across two or more lines
corresponding angles
angles in matching corners when a transversal cuts lines
alternate interior angles
angles inside the lines on opposite sides of the transversal
alternate exterior angles
angles outside the lines on opposite sides of the transversal
indirect proof
a proof where you assume the opposite and reach a contradiction
auxiliary line
an extra line drawn to help solve a problem or proof
Parallel Postulate
through a point not on a line, exactly one parallel line can be drawn
Euclidean geometry
geometry on a flat plane
non-Euclidean geometry
geometry on curved surfaces
triangle
a three-sided polygon
interior (triangle)
inside the triangle
exterior (triangle)
outside the triangle
vertex/vertices
a corner point where sides meet
sides (triangle)
the three line segments of a triangle
angles (triangle)
the three angles of a triangle
scalene
a triangle with all sides different
isosceles
a triangle with two equal sides
equilateral
a triangle with all equal sides
acute
an angle less than 90°
obtuse
an angle greater than 90°
right
a 90° angle
equiangular
a polygon with all angles equal
exterior angle
an angle formed by extending a side of a polygon
remote interior angles
the two interior angles not next to an exterior angle
corollary
a statement that follows easily from a theorem
polygon
a closed figure with straight sides
convex polygon
a polygon where all interior angles are less than 180°
consecutive vertices
vertices next to each other
consecutive sides
sides that share a vertex
diagonal
a segment connecting non-consecutive vertices
n-gon
a polygon with n sides
equilateral polygon
a polygon with all sides equal
equiangular polygon
a polygon with all angles equal
regular polygon
a polygon with all sides and angles equal