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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
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