geometry

point

an exact location with no size or dimension

line

a straight path that extends infinitely in both directions with no thickness

line segment

a part of a line that has two endpoints

ray

a part of a line that has one endpoint and extends infinitely in one direction

angle

a figure formed by two rays with a common endpoint (vertex)

vertical angles

a pair of opposite angles formed when two lines intersect

vertical angle theorem

vertical angles are congruent

complementary angles

two angles whose measures add up to 90

linear pair

a pair of adjacent angles whose non-shared sides form a straight line

supplementary

two angles are supplementary if the sum of their measures is 180

acute

an angle that measures less than 90

obtuse

an angle that measures greater than 90 but less than 180

right

an angle that measures exactly 90

plane

a flat , 2D surface that extends infinitely in all directions

angle bisector

a ray that divides an angle into two equal angles

segment bisector

a line, ray, or segment that passes through the midpoint of a segment, dividing it into two equal parts

adjacent angle

two angles that share a common side and a common vertex without overlapping

segment addition

stating that if point B is inbetween point A and C then AB + BC=AC

angle addition

states that if point D is inside angle ABC then angle ABD + angle DBC = angle ABC

linear angles

are two adjacent angles that form a straight line when their non common sides are opposite rays. together they add up to 180

inductive reasoning

a type of reasoning that makes generalizations based on observing patterns or specific examples

deductive reasoning

a type of reasoning that uses facts, definitions accepted properties and logical rules to reach a conclusion

counterexample

a single example that shows a statement or conjecture is false

conditional

a logical statement with two parts : a hypothesis and a conclusion (written in the form “ if P , then Q”)

converse

formed by switching the hypothesis and the conclusion

inverse

formed by negating both the hypothesis and the conclusion

contrapostive

formed by switching and negating both the hypothesis and the conclusion

reflexive property of congruence

a figure is always congruent to itself

symmetric property of congruence

if one figure is congruent to a second figure then the second figure is congruent to the first

transitive property of congruence

if one figure is congruent to a second figure and the second figure is congruent to the third and the first and third are congruent to each other. ( 1=2, 2=3, 1=3.)