#### Study sets matching "geometry chapter 6"

#### Study sets matching "geometry chapter 6"

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…

definition of a parallelogram

properties of a parallelogram

definition of a rectangle

definition of a rhombus

a quadrilateral with both pairs of opposite sides parallel

1. both pairs of opposite sides are congruent... 2. both pairs o…

a parallelogram with 4 right angles

a parallelogram with 4 congruent sides

definition of a parallelogram

a quadrilateral with both pairs of opposite sides parallel

properties of a parallelogram

1. both pairs of opposite sides are congruent... 2. both pairs o…

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.

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

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…

Altitude

angle bisector

base

centroid

A perpendicular segment in which one endpoint is a vertex of…

A ray whose endpoint is the vertex and is located in the inte…

The side opposite the vertex angle

The point of intersection of the 3 medians of a triangle

Altitude

A perpendicular segment in which one endpoint is a vertex of…

angle bisector

A ray whose endpoint is the vertex and is located in the inte…

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

base angles of a trapezoid

isosceles trapezoid

kite

midsegment of a trapezoid

each pair of adjacent angles to a base

whose nonparallel opposite sides are congruent.

is a quadrilateral with two pairs of congruent adjacent sides…

is the segment that joins the midpoints of the nonparallel op…

base angles of a trapezoid

each pair of adjacent angles to a base

isosceles trapezoid

whose nonparallel opposite sides are congruent.

concave

convex

isosceles trapezoid

kite

A polygon where part of the diagonal is in the exterior

A polygon where the entire diagonal is in the interior

Trapezoid where the legs are congruent

Quadrilateral with exactly two pairs of consecutive sides

concave

A polygon where part of the diagonal is in the exterior

convex

A polygon where the entire diagonal is in the interior

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…

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

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

Each pair of angles adjacent to a base.

The two parallel sides of a trapezoid.

Angles of a polygon that share a commo…

A polygon whose angles are all equal o…

Base Angles of a Trapezoid

Base of a Trapezoid

Consecutive Angles

Equiangular Polygon

Each pair of angles adjacent to a base.

Base Angles of a Trapezoid

The two parallel sides of a trapezoid.

Base of a Trapezoid

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

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

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…

base of a trapezoid

base angle of a trapezoid

concave

convex

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…

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

Parallelogram

Rectangle

Square

Kite

A quadrilateral with both pairs of opposite sides parallel

A parallelogram with four right angles

A parallelogram with four congruent sides and four right angles

A quadrilateral with two pairs of adjacent sides congruent an…

Parallelogram

A quadrilateral with both pairs of opposite sides parallel

Rectangle

A parallelogram with four right angles

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…

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)

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…

concurrent lines

circumcenter

incenter

median of a triangle

3 or more lines that intersect at one point

the point of concurrency of the perpendicular bisectores of t…

the point of concurrency of the angle bisectors

a segment from a vertex to the midpoint of the opposite side

concurrent lines

3 or more lines that intersect at one point

circumcenter

the point of concurrency of the perpendicular bisectores of t…

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…

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

Diagonal

Convex Polygon

Concave Polygon

A closed plane figure formed by three or more segments.

A segment that connects two nonconsecutive vertices.

No diagonal of a polygon contains points outside the polygon.…

A polygon with a diagonal contains points outside the polygon…

Polygon

A closed plane figure formed by three or more segments.

Diagonal

A segment that connects two nonconsecutive vertices.

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

Alternate Exterior Angles

Alternate Interior Angles

Congruent Circles

Congruent Quadrilaterals

Angles on the exterior of the two lines and on opposite sides…

Angles on the interior of the two lines and on opposite sides…

Circles with congruent radii

Quadrilaterals with all corresponding parts congruent

Alternate Exterior Angles

Angles on the exterior of the two lines and on opposite sides…

Alternate Interior Angles

Angles on the interior of the two lines and on opposite 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

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.

Perpendicular bisector theorem

Angle bisector theorem

Circumcenter

Incenter

-equidistant from the endpoints of the segment

-equidistant from the two sides of the angle

-equidistant from the vertices (angles) of the triangle... -perp…

-equidistant from the sides of a triangle... -always inside the…

Perpendicular bisector theorem

-equidistant from the endpoints of the segment

Angle bisector theorem

-equidistant from the two sides of the angle

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.

properties of inequalities

exterior angle inequality theorem

given if p then q; converse

given if p then q; converse

a>b, b>c, then a >c... a > b, c>0, then a+c > b+c... a> b, c> 0, th…

the exterior angle of a triangle is greater than either remot…

q then p

inverse not p then not q

properties of inequalities

a>b, b>c, then a >c... a > b, c>0, then a+c > b+c... a> b, c> 0, th…

exterior angle inequality theorem

the exterior angle of a triangle is greater than either remot…

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…

diameter

diagonal

right trapezoid

two-dimensional

a line segment drawn through the center of a circle with both…

a segment that connects any two vertices of the polygon but i…

a trapezoid with exactly two right angles

a figure that lies on a flat surface that has length and width

diameter

a line segment drawn through the center of a circle with both…

diagonal

a segment that connects any two vertices of the polygon but i…

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 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.

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 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

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…

Proportion

Means

Extremes

Geometric Mean

An equation that states that two ratios are equal

In a proportion, the denominator of the first equation and th…

In a proportion, the numerator of the first equation and the…

A positive number that satisfies the proportion a/x= x/b; x =…

Proportion

An equation that states that two ratios are equal

Means

In a proportion, the denominator of the first equation and th…