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Two points are symmetric with respect…

Two lines are parallel iff

Transversal

The Parallel Postulate

the line is the perpendicular bisector of the line segment co…

they lie in the same plane and do not intersect.

is a line that "goes across" -that is, "intersects" two or mo…

Through a point not on a line, there is exactly one line para…

Two points are symmetric with respect…

the line is the perpendicular bisector of the line segment co…

Two lines are parallel iff

they lie in the same plane and do not intersect.

def of reflection-symmetric figure, sy…

flip-flop theorem

segment symmetry theorem

side-switching theorem

a plane figure F is a ___-___ figure IFF there is a line M su…

if F and G are points/figures and the reflection over line L…

every segment has exactly 2 lines of symmetry:... 1) the line co…

if 1 side of an angle is reflected over the line containing t…

def of reflection-symmetric figure, sy…

a plane figure F is a ___-___ figure IFF there is a line M su…

flip-flop theorem

if F and G are points/figures and the reflection over line L…

Diagonal

Parallelogram

Rectangle

Rhombus

A segment that connects any two nonconsecutive verticies.

A quadrilateral with both pairs of opposite sides parallel.

A parallelogram with four right angles.

A parallelogram with all four sides congruent.

Diagonal

A segment that connects any two nonconsecutive verticies.

Parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Diagonal

Parallelogram

Rectangle

Rhombus

In a polygon, a segment that connects nonconsecutive vertices…

A quadrilateral with two pairs of parallel sides

A parallelogram with four right angles and two pairs of congr…

A parallelogram with all four sides congruent

Diagonal

In a polygon, a segment that connects nonconsecutive vertices…

Parallelogram

A quadrilateral with two pairs of parallel sides

concave

convex

decagon

Hexagon

polygon will always have an interior angle with a measure tha…

all interior angles are less than or equal to 180 degrees

10 sided

6sided

concave

polygon will always have an interior angle with a measure tha…

convex

all interior angles are less than or equal to 180 degrees

two polygons are _____ _____ if corres…

statement of proportionality

scale factor

perimeters of similar polygons (theorem)

similar polygons

if two polygons are similar, then the ratio of the lengths of…

if two polygons are similar, then the ratio of their perimete…

two polygons are _____ _____ if corres…

similar polygons

statement of proportionality

base of a trapezoid

base angle of a trapezoid

concave polygon

convex polygon

one of the two parallel sides of the trapezoid.

one of a pair of consecutive angles whose common side is a ba…

a polygon in which a diagonal can be drawn such that part of…

a polygon in which no diagonal contains points in the exterio…

base of a trapezoid

one of the two parallel sides of the trapezoid.

base angle of a trapezoid

one of a pair of consecutive angles whose common side is a ba…

parallelogram

rhombus

rectangle

square

a quadrilateral with both pair of opposite sides parallel

a parallelogram with four congruent sides

a parallelogram with four right angles

a parallelogram with four congruent sides and four right angles

parallelogram

a quadrilateral with both pair of opposite sides parallel

rhombus

a parallelogram with four congruent sides

polygon

vertex

diagonal

convex polygon

a closed plane figure formed by three or more segments.

the endpoint of two sides

a segment joining two nonconsecutive vertices

has no diagonal with points outside the polygon

polygon

a closed plane figure formed by three or more segments.

vertex

the endpoint of two sides

The sum of all angles is (n - 2) * 180.

The sum of all exterior angles is 360.

The sum of all one interior angle of a…

Congruent

Polygon Angle Sum Theorem

Polygon Exterior Angle Theorem

Polygon Interior Angle Sum Theorem

Diagonals of a Rectangle

The sum of all angles is (n - 2) * 180.

Polygon Angle Sum Theorem

The sum of all exterior angles is 360.

Polygon Exterior Angle Theorem

Midsegment

Midpoint

Perpendicular bisector

Equidistant

connects the midpoints of two sides in a triangle. It is para…

A point that divides a segment into two congruent pieces (in…

A line that is perpendicular to a segment at its midpoint (cu…

The same distance

Midsegment

connects the midpoints of two sides in a triangle. It is para…

Midpoint

A point that divides a segment into two congruent pieces (in…

Quadrilateral

Special Quadrilaterals

Parallelogram

6 Properties of Parallelogram

any four-sided polygon

quadrilaterals that have certain properties

a quadrilateral with both pairs of opposite sides parallel

A quadrilateral with both pairs of opposite sides parallel... -…

Quadrilateral

any four-sided polygon

Special Quadrilaterals

quadrilaterals that have certain properties

perpendicular uniqueness theorem (plane)

perpendicular bisector (plane)

PBT (plane)

PBT Corollary

in a given plane, through a given point of a given line, ther…

of a segment is the line that is perpendicular to the segment…

the perpendicular bisector of a segment is the set of all poi…

given a segment and a line in the same plan, if two pints of…

perpendicular uniqueness theorem (plane)

in a given plane, through a given point of a given line, ther…

perpendicular bisector (plane)

of a segment is the line that is perpendicular to the segment…

Polygon

Regular

Irregular

Sum of interior angles of a polygon

A closed plane figure formed by 3 or more segments that inter…

Equilateral and equiangular

Not equilateral or equiangular

(n-2)(180)

Polygon

A closed plane figure formed by 3 or more segments that inter…

Regular

Equilateral and equiangular

Midsegment

Midpoint

Perpendicular Bisector

Equidistant

connects the midpoint of two sides in a triangle. It is paral…

a point that divides a segment into congruent pieces (in half)

a line that is perpendicular to a segment at its midpoint (cu…

the same distance

Midsegment

connects the midpoint of two sides in a triangle. It is paral…

Midpoint

a point that divides a segment into congruent pieces (in half)

x-axis

y-axis

origin

coordinate

horizontal line of the coordinate plane

the vertical line of the coordinate plane

the point which the x and y axis intersect perpendicularly

every point on a plane that can be described by 2 numbers

x-axis

horizontal line of the coordinate plane

y-axis

the vertical line of the coordinate plane

polygon

diagonal of a polygon

parallelogram

rhombus

A closed plane figure made up of line segments

a segment that joins two nonconsecutive vertices

A quadrilateral with two pairs of parallel sides

a parallelogram with 4 congruent sides

polygon

A closed plane figure made up of line segments

diagonal of a polygon

a segment that joins two nonconsecutive vertices

Diagonal

Polygon Interior Angles Sum

Polygon Exterior Angles Sum

Parallelogram

A segment in a polygon that connects a vertex with another ve…

The sum of the interior angle measures of a convex polygon wi…

The sum of the exterior angle measures of a convex polygon, o…

A quadrilateral that has two pairs of parallel sides

Diagonal

A segment in a polygon that connects a vertex with another ve…

Polygon Interior Angles Sum

The sum of the interior angle measures of a convex polygon wi…

Polygon Angle-Sum Theorem

Corollary to the Polygon Angle-Sum The…

Polygon Exterior Angle-Sum Theorem

parallelogram

the sum of the measures of a n-gon is (n-2)180

the measure of each interior angle of a regular polygon is (n…

the sum of the measures of the exterior angles of a convex po…

a quadrilateral whose opposite sides are both parallel and eq…

Polygon Angle-Sum Theorem

the sum of the measures of a n-gon is (n-2)180

Corollary to the Polygon Angle-Sum The…

the measure of each interior angle of a regular polygon is (n…

The parallel postulate

Theorem 16

Theorem 17

Corollary to theorem 17

Through a point not on a line, there is exactly one line para…

In a plane, two points each equidistant from the endpoints of…

Equal corresponding angles mean that lines are parallel.

Equal alternate interior angles mean that lines are parallel

The parallel postulate

Through a point not on a line, there is exactly one line para…

Theorem 16

In a plane, two points each equidistant from the endpoints of…

similar polygons≅⊥

is similar to symbol

Corresponding vertices are listed in _…

corresponding angles similar

Two polygons are similar polygons if corresponding angles are…

ABCD is similar --> EFGH or ABCD ~ EFGH

the same order

<A ≅ <E... <B ≅ <F... <C ≅ <G... <D ≅ <H

similar polygons≅⊥

Two polygons are similar polygons if corresponding angles are…

is similar to symbol

ABCD is similar --> EFGH or ABCD ~ EFGH

Midsegment (6.4)

Midpoint (1.3)

Perpendicular Bisector (6.1)

Equidistant (6.1)

Connects the midpoints of two sides in a triangle. It is para…

A point that divides a segment into two congruent pieces (in…

A line that is perpendicular to a segment at its midpoint (cu…

The same distance.

Midsegment (6.4)

Connects the midpoints of two sides in a triangle. It is para…

Midpoint (1.3)

A point that divides a segment into two congruent pieces (in…

Theorem 16

Theorem 17

Corollary 1 to Theorem 17

Corollary 2 to Theorem 17

In a plane, two points each equidistant from the endpoints of…

Equal Corresponding angles mean that lines are parallel

Equal alternate interior angles mean that lines are parallel

Supplementary interior angles on the same side of a transvers…

Theorem 16

In a plane, two points each equidistant from the endpoints of…

Theorem 17

Equal Corresponding angles mean that lines are parallel

SSS

SAS

ASA

AAS

Three sides of one triangle are congruent to three sides of a…

Two sides and the included angle of one triangle are congruen…

Two angles and the included side of one triangle are congruen…

Two angles and the non-included side of one triangle are cong…

SSS

Three sides of one triangle are congruent to three sides of a…

SAS

Two sides and the included angle of one triangle are congruen…

Base of a Trapezoid

Base Angle of a Trapezoid

Diagonal

Isosceles Trapezoid

The one pair of parallel sides.

Angles that connect the base to the leg.

This is in polygons with three sides or more connecting any t…

If the legs are congruent; both pairs of base angles are cong…

Base of a Trapezoid

The one pair of parallel sides.

Base Angle of a Trapezoid

Angles that connect the base to the leg.

Polygon Angle Sum Theorem

Corollary to the Polygon Angle Sum The…

Polygon Exterior Angle-Sum Theorem

If three or more parallel lines cut of…

The sum of the measures of the interior angles of an n-gon is…

The measure of each interior angle of a regular n-gon is (n-2…

The Sum of the measures of the exterior angles of a polygon,…

Then they cut off congruent segments on every transversal.

Polygon Angle Sum Theorem

The sum of the measures of the interior angles of an n-gon is…

Corollary to the Polygon Angle Sum The…

The measure of each interior angle of a regular n-gon is (n-2…

polygon

diagonal of a polygon

quadrilateral

parallelogram

A plane figure that is formed by three or more segments calle…

A segment that joins two nonconsecutive vertices of a polygon.

A polygon with four sides.

A quadrilateral with both pairs of opposite sides parallel.

polygon

A plane figure that is formed by three or more segments calle…

diagonal of a polygon

A segment that joins two nonconsecutive vertices of a polygon.

diagonal

parallelogram

rectangle

rhombus

a segment that connects any two nonconsecutive vertices

a quadrilateral with both pairs of opposite sides parallel

a parallelogram with four right angles

a parallelogram with all four sides congruent

diagonal

a segment that connects any two nonconsecutive vertices

parallelogram

a quadrilateral with both pairs of opposite sides parallel

Diagonal

Parallelogram

Rhombus

Rectangle

A segment that connects two nonconsecutive vertices.

A quadrilateral with both pairs of opposite side parallel.

A parallelogram with four congruent sides.

A parallelogram with four right angles.

Diagonal

A segment that connects two nonconsecutive vertices.

Parallelogram

A quadrilateral with both pairs of opposite side parallel.

diagonal

Polygon Interior Angles Sum Theorem

Polygon Exterior Angles Sum Theorem

parallelogram

A segment that connects any two non-consecutive vertices

The sum of the interior angle measures of an n-sided convex p…

The sum of the exterior angles measures of a convex polygon,…

A quadrilateral with both pairs of opposite sides parallel

diagonal

A segment that connects any two non-consecutive vertices

Polygon Interior Angles Sum Theorem

The sum of the interior angle measures of an n-sided convex p…

altitude of a triangle

Centroid

Circumcenter

Concurrent

The perpendicular segment from a vertex of a ... triangle to the…

The point of concurrency of the three medians of a triangle.

The point of concurrency of the three ... perpendicular bisector…

Three or more lines, rays, or segments that ... intersect in the…

altitude of a triangle

The perpendicular segment from a vertex of a ... triangle to the…

Centroid

The point of concurrency of the three medians of a triangle.

Acute angle

Adjacent angles

Base of a parallelogram

base of a triangle

An acute angle is an angle with a measure between 0 degrees a…

Adjacent angles share a vertex and a side but have no interio…

The height of a parallelogram is the length of a perpendicula…

Any side of a triangle can be considered the base of a triang…

Acute angle

An acute angle is an angle with a measure between 0 degrees a…

Adjacent angles

Adjacent angles share a vertex and a side but have no interio…

If two numbers or quantaties and b is…

An equation that states that two ratio…

The ___ ____ of two positive numbers a…

Cross Products property, If a/b=c/d wh…

ratio of a to b

proportion, means, extremes

geometric mean

ad=bc

If two numbers or quantaties and b is…

ratio of a to b

An equation that states that two ratio…

proportion, means, extremes

Angle-Angle similarity Theorem

Angle-bisector/ Proportional side theo…

Geometric Mean

Dilation

two triangles are similar if they have two corresponding angl…

If a ray bisects an angle of a triangle then it divides the o…

The central number in a geometric progression

Transformation that produces an image that is the same shape…

Angle-Angle similarity Theorem

two triangles are similar if they have two corresponding angl…

Angle-bisector/ Proportional side theo…

If a ray bisects an angle of a triangle then it divides the o…

corresponding angles

obtuse angle

transversal line

parallel lines

Angles in the same place on different lines

An angle between 90 and 180 degrees

a line that intersects two lines

lines in the same plane that do not intersect

corresponding angles

Angles in the same place on different lines

obtuse angle

An angle between 90 and 180 degrees

polygon

vertex of a polygon

consecutive vertices

diagonal

A closed plane figure formed by three or more line segments t…

the point where two sides of a polygon meet

two vertices that are endpoints of the same side of a polygon

A line segment connecting non-adjacent nonconsecutive vertice…

polygon

A closed plane figure formed by three or more line segments t…

vertex of a polygon

the point where two sides of a polygon meet

Similar polygons

Scale Factor

Perimeters of Similar Polygons

Corresponding lengths in similar polyg…

Polygons whose corresponding angles are congruent and whose c…

If two polygons are similar, then the ratio of the lengths of…

If two polygons are similar, then the ratio of their perimete…

if two polygons are similar, then the ratio of any two corres…

Similar polygons

Polygons whose corresponding angles are congruent and whose c…

Scale Factor

If two polygons are similar, then the ratio of the lengths of…

base of a prism

dihedral angle

edge of a polyhedron

edge of a dihedral angle

A face formed by the polygonal region or its image.

The figure formed by two half-planes with a common edge.

The segment formed by the intersection of two faces of a poly…

The intersection of the half-planes of a dihedral angle.

base of a prism

A face formed by the polygonal region or its image.

dihedral angle

The figure formed by two half-planes with a common edge.

Inscribed angle conjecture

Inscribed angles intersecting arcs

Angles inscribed in a semicircle

Parallel lines intercepted arcs conjec…

The measure of an inscribed angle is 1/2 the intercepted arc

Inscribed angles that intercept the same arc are congruent

Angles inscribed in a semicircle are right angles

The arcs between a pair of parallel lines are congruent

Inscribed angle conjecture

The measure of an inscribed angle is 1/2 the intercepted arc

Inscribed angles intersecting arcs

Inscribed angles that intercept the same arc are congruent

Base

Base Angle of a trapezoid

Diagonal

Isosceles Trapezoid

The parallel sides of a trapezoid.

Trapezoid angles formed by the base and one of the legs.

In a polygon, a segment that connects nonconsecutive vertices…

A trapezoid in which the legs are congruent, both pairs of ba…

Base

The parallel sides of a trapezoid.

Base Angle of a trapezoid

Trapezoid angles formed by the base and one of the legs.

Polygon

Consecutive Angles

Bases of a Trapezoid

Legs of a Trapezoid

A closed plane figure formed by three or more segments.

Angles of a polygon that share a side and are supplementary.

The parallel sides of a trapezoid.

The nonparallel sides of a trapezoid.

Polygon

A closed plane figure formed by three or more segments.

Consecutive Angles

Angles of a polygon that share a side and are supplementary.

base angle of a trapezoid

base of a trapezoid

concave (polygon)

convex (polygon)

Two consecutive... angles whose... common side is a... base

Each of the parallel... sides of a trapezoid

If any part of a diagonal... contains points in the... exterior of…

If no diagonal contains... points in the exterior

base angle of a trapezoid

Two consecutive... angles whose... common side is a... base

base of a trapezoid

Each of the parallel... sides of a trapezoid

congruent

congruent angles

congruent segments

congruent triangles

having the exact same size and shape

angles that have equal measures

segments that have the same length

triangles whose corresponding angles and sides are congruent

congruent

having the exact same size and shape

congruent angles

angles that have equal measures

def of trapezoid

def of isosceles trapezoid

quadrilateral hierarchy theorem

kite symmetry theorem

a quadrilateral is a ___ IFF it has at least 1 pair of // sides

a trapezoid is an ___ ___ IFF it has a pair of base angles =…

the line containing the ends of a kite is a symmetry line for…

def of trapezoid

a quadrilateral is a ___ IFF it has at least 1 pair of // sides

def of isosceles trapezoid

a trapezoid is an ___ ___ IFF it has a pair of base angles =…

parallel postulate

In a plane, two points equidistant fro…

Equal corresponding angles mean that

Equal alternate interior angles mean t…

through a point not on a line, there is exactly one line para…

determine the perpendicular bisector of the line segment

lines are parallel

lines are parallel

parallel postulate

through a point not on a line, there is exactly one line para…

In a plane, two points equidistant fro…

determine the perpendicular bisector of the line segment

Base of a Trapezoid

Base Angle of a Trapezoid

Diagonal

Isosceles Trapezoid

The one pair of parallel sides.

Angles that connect the base to the leg.

This is in polygons with three sides or more connecting any t…

If the legs are congruent; both pairs of base angles are cong…

Base of a Trapezoid

The one pair of parallel sides.

Base Angle of a Trapezoid

Angles that connect the base to the leg.

Two polygons are similar if...

Scale factor

Perimeters of similar polygons theorem

Transformation

their corresponding angles are congruent and their correspond…

ratio of two corresponding side lengths in similar figures

if two polygons are similar the ratio of the perimeters are t…

An operation that moves or changes a geometric figure in some…

Two polygons are similar if...

their corresponding angles are congruent and their correspond…

Scale factor

ratio of two corresponding side lengths in similar figures