Geometry Vocab

acute angle

an angle that measures greater than 0 degrees and less than 90 degrees

alternate exterior angles

for two lines intersected by a transversal, a pair of angles that lie on opposite sides of the transversal and outside the other two lines

alternate interior angles

for two lines intersected by a transversal, a pair of nonadjacent angles that lie on opposite sides of the transversal and between the other two lines

angle

two rays that meet at a point

angle bisector

a ray that divides an angle into two congruent angles

biconditional

a combination of two conditional statements

collinear

points that lie on the same line

complementary angles

two angles whose measures have a sum of 90 degrees

conditional statement

a statement that can be written in the form "if p, then q" where p is the hypothesis and q is the conclusion

congruent

having the same size and shape

conjecture

a statement that is believed to be true

contrapositive

the hypothesis and the conclusion in a conditional statement are opposed, and then swapping the order

converse

the statement formed by exchanging the hypothesis and conclusion of a conditional statement

coplanar

points that lie in the same plane

counterexample

an example that proves that a conjecture or statement is false

deductive reasoning

the process of using logic to draw conclusions

image

a shape that results from a transformation of a figure known as the preimage

inductive reasoning

the process of reasoning that a rule or statement is true because specific cases are true

isometry (rigid motion)

a transformation that does not change the size or shape of a figure

leg of a right triangle

one of the two sides of the right triangle that form the right angle

line

an undefined term in geometry, a line is a straight path that has no thickness and extends forever

line of symmetry

a line that divides a plane figure into two congruent reflected halves

line segment

a part of a line consisting of two endpoints and all points between them

line symmetry

a figure that can be reflected across a line so that the image coincides with the preimage

linear pair

a pair of adjacent angles whose noncommon sides are opposite rays

midpoint

the point that divides a segment into two congruent segments

noncollinear

points that do not lie on the same line

obtuse angle

an angle between 90 and 180 degrees

opposite rays

two rays that have a common endpoint and form a line

parallel

lines that never intersect or touch

perpendicular bisector

a line perpendicular to a segment at the segment's midpoint

perpendicular lines

lines that intersect at 90 degrees

plane

an undefined term in geometry, it is a flat surface that has no thickness and extends forever.

point

an undefined term in geometry, it names a location and has no size

postulate

a statement that is accepted as true without proof

preimage

the original figure in a transformation

ray

a part of a line that starts at an endpoint and extends forever in one direction

reflection

a transformation across a line, called the line of reflection, such that the line of reflection is the perpendicular bisector of each segment joining each point and its image

right angle

an angle that measures 90 degreees

rotation

a transformation about a point, also known as the center of rotation, such that each point and its image are the same distance from it. all of the angles with the same vertex are congruent

rotational symmetry

a figure that can be rotated about a point by an angle less that 360 degrees so that the image coincides with the preimage has rotational symmetry

same-side interior angles

for two lines intersected by a transversal, a pair of angles that lie on the same side of the transversal and between the two lines

segment bisector

a line, ray, or segment that divides a segment into two congruent segments

straight angle

an angle of 180 degrees

supplementary angles

two angles whose measures have a sum of 180 degrees

symmetry

in the transformation of a figure such that the image coincides with the preimage, the image and preimage have symmetry

theorem

a statement that has been proven

transformation

a change in the position, size, or shape of a figure or graph

translation

a transformation that shifts or slides every point of a figure or graph the same distance in the same direction

transversal

a line that intersects two coplanar lines at two different points

undefined term

a basic figure that is not defined in terms of other figures. the undefined terms in geometry are point, line, and plane

vector

a quantity that has both magnitude and direction

vertex

the point of intersection of two rays

vertical angles

the nonadjacent angles formed by two intersecting lines