# Vocab Terms & Theorems/Postulates

## 116 terms

### acute angle

an angle with a degree measure less than 90 degrees

### acute triangle

a triangle in which all of the angles are acute angles

two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points

### alternate exterior angles

with two parallel lines cut by a transversal the two outermost opposite angles

### alternate interior angles

with two parallel lines cut by a transversal the two opposite inner angles

### angle

the intersection of two noncollinear rays at a common endpoint. Rays are called sides and the endpoint called the vertex

### angle bisector

a ray that divides an angle into two congruent angles

### base angles

the four angles of a isosceles Trapezoid that are all congruent and the two congruent angles in an isosceles triangle

### biconditional

the conjunction of a conditional statement and its converse

### collinear

points that lie on the same plane

### complementary angles

two angles with measures that have a sum of 90

### congruence transformations

a mapping for which a geometric figure and its image are congruent. Examples include flip, slide, and turn

### congruent

having the same measure

### congruent triangles

triangles that have their corresponding parts congruent

### conjecture

an educated guess based on known information

### conjunction

a compound statement formed by joining two or more statements with the word and

### consecutive interior angles

with two parallel lines cut by a transversal the inner same sided angles

### contrapositive

the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

### converse

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

### coordinate proof

a proof that uses figures in the coordinate plane and algebra to prove geometric concepts

### coplanar

points that lie in the same plane

### corollary

a statement that can be easily proved using a theorem

### corresponding angles

with two parallel lines cut by a transversal the angles that relate with one another and are congruent

### counterexample

an example used to show that a given statment is not always true

### deductive reasoning

a system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions

### diagonals

in a polygon a segement that connects nonconsecutive vertices of the polygon

### disjunction

a compound statement formed by joining two or more statements with the word or

### equiangular triangle

a triangle with all angles congruent

equal distance

### equilateral triangle

a triangle with all sides congruent

### exterior angle

an angle formed by one side of a triangle and the extension of another side

### flow proof

a proof that organizes statements in logical order, starting with the given statements and using boxes and arrows

### if-then statement

a compound statement of the form "if A, then B" where A and B are the statements

### included angle

in a triangle the angle formed by two sides

### included side

the sie of a triangle that is a side of each of two angles

### inductive reasoning

reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction

### inverse

the statement formed by negating both the hypothesis and conclusion of a conditional statement

### isosceles trapezoid

a trapezoid in which the legs are congruent, both pairs of base angles are congruent, and the diagonals are congruent

### isosceles triangle

a triangle with at least two sides congruent

### Law of Detachment

if p to q is a true conditional and p is true, then q is also true

### Law of Syllogism

if p to q and q to r are true conditionals then p to r is also true

### line segment

a measurable part of a line that consists of two points, called endpoints, and all of the points between them

### linear pair

a pair of adjacent angles whose non-common sides are opposite rays

### logically equivalent

statements that have the same truth values

### median

In a trapezoid the segment that joins the midpoints of the legs

### midpoint

the point halfway b/w the endpoints of a segment

### negation

if a statement is represented by p, then this is not p of the statement

### obtuse angle

an angle with degree measure greater than 90 but less than 180

### obtuse triangle

a triangle with an obtuse angle

### paragraph proof

an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true

### parallel lines

coplanar lines that do not intersect

### parallel planes

planes that do not intersect

### parallelogram

a quadrilateral with parallel opposite sides

### perimeter

the sum of the lengths of the sides of a polygon

### perpendicular line

line that forms right angles

y-y1 = m(x-x1)

### polygon

a closed figure formed by a finite number of coplanar segments called sides and the sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their endpoints, called the vertices

### postulate

a statement that describes a fundamental relationship b/w the basic terms of geometry. Accepted as true

### rate of change

describes how a quantity is changing over time. Change in y over change in x to solve

### ray

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

### rectangle

a quadrilateral with four right angles

### remote interior angles

the angles of a triangle that are not adjacent to a given exterior angle

### rhombus

a quadrilateral with all four sides congruent

### right angle

an angle with the measure of 90 degrees

### right triangle

a triangle with a right angle with opposite side the hypotenuse and the other two sides are legs

### scalene triangle

a triangle with no two sides congruent

### segment bisector

a segment, line, or plane that intersects a segment at its midpoint

### skew lines

lines that do not intersect and are not coplanar

### slope

change in y over change in x

y = mx + b

### square

a quadrilateral with four right angles and four congruent sides

### statement

any sentence that is either true or false, but not both

### supplementary angles

two angles with measure that have a sum of 180

### theorem

a statement/conjecture that can be proven true by undefined terms, definitions, and postulates

### transversal

a line that intersects two or more lines in a plane at different points.

### trapezoid

a quadrilateral with one pair of parallel sides.

### truth table

a table used as a convenient method for organizing the truth values of statements

### truth value

the truth/falsity of a statement

### two-column proof

a formal proof that contains statements and reasons organized in two columns.

### vertex angle

main angle in a triangle

### vertical angles

two nonadjacent angles formed by two intersecting lines

if R is in the interior of angle PQS then the m of PQR + m of RQS = m of PQS. and vice versa

### Complement Theorem

If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles

### Supplement Theorem

if two angles form a linear pair, then they are supplementary angles

### Vertical Angle Theorem

if two angles are vertical angles, then they are congruent

### Alternate exterior angles Theorem

if two parallel lines are cut by a transversal, then each pair of alt exterior angles are congruent

### Alternate Interior angles Theorem

if two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent

### Corresponding angles Postulate

if two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent

### Consecutive Interior Angles Theorem

if two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary

### Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other

### Parallel Postulate

if there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line

### Angle Sum Theorem

the sum of the measures of hte angles of a triangle is 180

### Third Angle Theorem

if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent

### Angle Angle Side Theorem AAS

if two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle then the two triangles are congruent.

### Exterior Angle Theorem

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles

### Side Side Side Congruence SSS

if the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent

### Side Angle Side Congruence SAS

if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then they are congruent

### Angle Side Angle Theorem ASA

if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the two triangles are congruent.

### Leg Leg Congruene LL

if the legs of one right triangle are congruent to the corresponding legs of another right triangle, they are congruent

### Hypotenuse Angle Congruence HA

if the hypotenuse and acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then they are congruent

### Leg Angle Congruence LA

If one leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then they are congruent

### Hypotenuse Leg Congruence HL

if the hypotenuse and a leg of one right triangle are congruent to the same parts of another triangle then they are congruent

S = 180(n-2)

sum equals 360

r = r

m = j, j = m

### Transitive Property of Congruence/Equality

s = t, t = u, s = u

### Properties of Parallelograms

Opposite sides and angles are congruent, consecutive angles are supplementary, if it has one right angle it has all right angles, diagonals bisect each other and separate it into two congruent triangles,

if both pairs of opposite sides and angles are congruent then it is a parallelogram, if diagonals bisect each toehr and if one pair of opposite sides is parallel and congruent, then it is a parallelogram

### Properties of Rectangles

All four angles are right angles, opposite sides are congruent and parallel, opposite angles are congruent, cons angles supplementary, diagonals congruent bisectors,

### Properties of Rhombi

all the properties of parallelograms and quadrilaterals plus: The diagonals are perpendicular, each diagonal bisects a pair of opposite angles

### Properties of Squares

all properites of parallelograms, quadrilaterals, rectangles and rhombi

### Properties of Trapezoids

both pairs of base angles of an isosceles trapezoid are congruent as well as the diagonals, and the median is parallel to the bases and its measure is one half the sum of hte measures of the bases

### Midpoint Theorem

if M is the midpoint of segment AB then segment AB is congruent to segment MB