Geometry Midterms

An __ is a transformation about a point with a given angle measure

rotation

Reflections, Translations, Rotations, and Glide Reflections are the four types of ___

Rigid Motions

A line that a figure is reflected across so that it maps onto itself is called an ___

Line of Symmetry

The Composition of a reflection and a translation is called a

Glide reflection

The set of points that a transformation acts on is the __

Pre-image

The result of a transformation is called the _

Image

A statement accepted without proof is a __

Postulate

Arriving at a conclusion by observing patterns is ___

Inductive Reasoning

A __ is the combination of a conditional and its converse

bi-conditional

According to the ___, if a conditional statement and its hypothesis is true, then its conclusion is also true

Law of Detachment

A conjuncture that has been proven is a ___

theorem

A statement of the form if not Q, then not P is a ___ of the conditional if p, then q

Contra-positive

You use ___ when you logically come to a valid conclusion based on given statements

deductive reasoning

Angles that are outside the space between parallel lines and that lie on the same side of a transversal are __

Same Side interior Angles

A ___ intersects co-planar lines at distinct points

transversal

Two angles inside a triangle that correspond to the nonadjacent exterior angle are the

remote interior angles

___ lie on the same side of a transversal of parallel lines and are in corresponding positions relative to the parallel lines.

Corresponding Angles

Angles between parallel lines that are nonadjacent and that lie on opposite sides of a transversal are

Alternate interior angles

Angles Between parallel lines that are on the same side of a transversal are

Same-side interior angles

Figures that have the same size and shape are said to be ___

congruent

The side of an isosceles triangle that is opposite the vertex is called the _

Base

A rigid motion is sometimes called a __ because it maps a figure with the same shape and size

(congruence) transformation

The legs of a isosceles triangle form an angle called the

Vertex

Colinear Points

Points that all lie on the same line

Line

A one-dimensional, forever going line. When two points are on it, they make a segment of the line.

Plane

A two dimensional surface with no boundaries

Point

A point in space

Segment Addition Postulate

AB+BC=AC

Angle Addition Postulate

m∠ABC+m∠DBC = m∠ABD

Angle Bisector

An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.

Segment Bisector

A segment bisector is a line, a ray, a line segment, or a point that cuts a line segment at the center dividing the line into two equal parts.

Midpoint

The midpoint of a line segment is the point at the exact middle of the line segment. The midpoint splits the line segment into two parts of the exact same measure

Midpoint Formula

(x1+x2 /2) , (Y1+Y2 /2)

Sequence

A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term.

conjecture

An unproven guess.

Conditional

Conditional Statement: A statement with a hypothesis followed by a conclusion. Can be written in “if-then” form.

Converse

A statement where the hypothesis and conclusion of a conditional statement are switched.

Inverse

The inverse of a conditional statement is when both the hypothesis and conclusion are negated; the “If” part or p is negated and the “then” part or q is negated. The Inverse is referred to as ~p → ~q where ~ stands for NOT or negating the statement.

Linear Pair

The definition of a linear pair is two angles that make a straight line when put together. A linear pair also follows the linear pair postulate which says the angles add up to 180°.

Triangle Angle Sums

are always 180 Degrees

Perpendicular Bisector

A perpendicular bisector has two requirements: perpendicular and bisector. Perpendicular lines or line segments intersect at right, or 90 degree, angles.

Orientation

Orientation is how the relative pieces of an object are arranged