61 terms

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