61 terms

Geometry Vocab

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bisector (of a segment)
a point, line, ray, or segment that intersects a segment at its midpoint
angle
two rays with a common endpoint (vertex)
acute angle
less than 90 degrees
right angle
90 degrees
obtuse angle
between 90 and 180 degrees
straight angle
180 degrees
reflex angle
greater than 180 degrees
adjacent angles
2 angles with a common vertex, common side, and no common interior points
3 methods of naming angles
3 letter name, 1 letter name, number
space
set of all points (3D)
collinear
contained on the same line
coplanar
contained on the same plane
segment
a portion of a line with 2 endpoints
ray
a portion of a line with 1 endpoint
opposite rays
collinear rays that share endpoints but no other points
postulate
a statement that is accepted as true (no proof)
theorem
a statement that is proved
congruent segments
segments that have the same length
midpoint
a point that divides a segment into 2 congruent segments
parallelogram
a quadrilateral with both pairs of opposite sides parallel
rhombus
a parallelogram with 4 congruent sides
square
a parallelogram with 4 congruent sides and four right angles
trapezoid
a quadrilateral with exactly 1 pair of parallel sides (legs not parallel)
isosceles trapezoid
a trapezoid with congruent legs
kite
a quadrilateral with 2 pairs of congruent sides, but opposite sides are not congruent
isosceles triangle
a triangle with at least 2 congruent sides
equilateral triangle
a triangle with all sides congruent
right triangle
a triangle with 1 right angle
midpoint theorem
the midpoint of a segment divides the segment into 2 parts, each half of the original
angle bisector theorem
an angle bisector divides an angle into 2 parts, each half of the original
complementary
2 angles whose measures have a sum of 90 degrees
suplementary
2 angles whose measures have a sum of 180 degrees
WESOP
a whole equals the sum of its parts
important right triangle ratios
3:4:5, 5:12:13, 8:15:17
important theorem
through any two points there is exactly one line
right angle theorem
all right angles are congruent
vertical angle theorem
vertical angles are congruent
perpendicular lines intersecting theorem
perpendicular lines intersect to form congruent, adjacent angles (converse: if two lines intersect to form congruent, adjacent angles, then they are perpendicular)
complementary congruence theorem
if two angles are complementary to congruent angles, then they are congruent to each other
supplementary theorem
if the exterior sides of two adjacent angles form a straight angle, then the angles are supplementary
exterior of perpendicular=complementary theorem
if the exterior sides of two adjacent angles are perpendicular, then the angles are complementary
parallel planes by a third
if two parallel planes are cut by a third plane, their intersections are parallel lines
2 parallel alt. int.
if two parallel lines are cut by a transversal, alternate interior angles are congruent
2 parallel ssi
if two parallel lines are cut by a transversal, same side interior angles are supplementary
TV perpendicular to parallel
if a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other
2 parallel alt. ex.
if two parallel lines are cut by a transversal, alternate exterior angles are congruent
2 lines and alt int then...
if two lines are cut by a transversal and alternate interior angles are congruent, the lines are parallel
2 lines and ssi then...
if two lines are cut by a transversal and same side interior angles are supplementary, the lines are parallel
in a plane 2 lines perpendicular
in a plane, two lines perpendicular to the same line are perpendicular to each other
2 lines same line
if two lines parallel to the same line then they are parallel to each other
through a point not on a line... parallel line
through a point not on a line, there exists exactly one line parallel to the given line
through a point not on a line... perpendicular line
through a point not on a line, there exists exactly one line perpendicular to the given line
the sum of triangle
the sum of the measures of a triangle = 180
angle measure equiangular triangle
each angle of an equiangular triangle = 60
2 triangles 2 angles whats the third
if 2 angles on a triangle are congruent to 2 angles of another triangle, then 3rd angles are congruent
the acute of rt triangles
the acute angles of a right triangle are complementary
triangle rules
a triangle can have at most 1 right or 1 obtuse angle
exterior angle of a triangle = sum of ...
the measure of an exterior angle of a triangle = sum of 2 remote interior angles
the sum of the measures of the interior angles of an n-gon is...
180(n-2)
the measure of each interior angle of a regular n-gon is...
(n-2)180/n
the sum of the measures of the exterior angles of a polygon is...
360