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

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

Secant Tangent Thrm

Two Intersecting Chords Thrm

Tangent Chord Angle Thrm

Two Intersecting chords thrm proof tip

Outside angle = 1/2 (Difference of Intercepted Arcs)

Angle formed = 1/2 (Sum of Intercepted Arcs)

Tangent Chord Angle = 1/2 Intercepted Arc

Draw triangle and use exterior angle of triangle thrm

Secant Tangent Thrm

Outside angle = 1/2 (Difference of Intercepted Arcs)

Two Intersecting Chords Thrm

Angle formed = 1/2 (Sum of Intercepted Arcs)

polygon

square

rhombus

quadrilateral

A closed plane figure made up of line segments

A quadrilateral with 4 sides that are equal and has all 90 de…

A parallelogram with 4 congruent sides.

4 sided polygon

polygon

A closed plane figure made up of line segments

square

A quadrilateral with 4 sides that are equal and has all 90 de…

Midsegment

Midpoint

Perpendicular Bisector

Eqidistant

A segment that connects the midpoints of two sides of a trian…

A point that divides a segment into two congruent segments.

A line that is perpendicular to a segment at its midpoint.

The same distance.

Midsegment

A segment that connects the midpoints of two sides of a trian…

Midpoint

A point that divides a segment into two congruent segments.

altitude

angle bisector

median

perpendicular bisector

goes from the vertex to the opposite side at 90 degrees

splits one angle into two congruent angles

line from the vertex to the midpoint

intersects midpoint at 90 degrees (doesn't always go through…

altitude

goes from the vertex to the opposite side at 90 degrees

angle bisector

splits one angle into two congruent angles

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…

midsegment

midpoint

Perpendicular bisector

equidistant

connects the midpoint of two triangles. It is parallel to and…

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

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

the same distances

midsegment

connects the midpoint of two triangles. It is parallel to and…

midpoint

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

Polygon Angle-Sum Theorem

Equilateral Polygon

Equiangular Polygon

Regular Polygon

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

A polygon with all sides congruent.

A polygon with all angles congruent.

A polygon that is both equilateral and equiangular.

Polygon Angle-Sum Theorem

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

Equilateral Polygon

A polygon with all sides congruent.

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…

Midsegment

Midpoint

Perpendicular Bisector

Equidistant

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

A point that divides a segment in two congruent pieces.

A line that is perpendicular to a segment at its midpoint.

The same distance.

Midsegment

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

Midpoint

A point that divides a segment in two congruent pieces.

Perpendicular bisector

Angle bisector

Circumcenter

Incenter

The line that is perpendicular to a segment at its midpoint

A ray that divides an angle into two congruent adjacent angles

The intersection of perpendicular bisectors in a triangle

Point where all angle bisectors intersect... Equidistance from a…

Perpendicular bisector

The line that is perpendicular to a segment at its midpoint

Angle bisector

A ray that divides an angle into two congruent adjacent angles

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…

similar polygons

scale factor

Perimeters of Similar Polygons

Dilation

if corresponding angles are congruent and corresponding side…

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

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

an image that preserves angle measures and results in an imag…

similar polygons

if corresponding angles are congruent and corresponding side…

scale factor

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

means and extremes

Geometric mean

1. Reciprocal property

2.

a and b are the positive numbers that x satisfy

if 2 ratios are equal, then their reciprocals are also equal

if you interchange the means of a proportion, then you form a…

means and extremes

Geometric mean

a and b are the positive numbers that x satisfy

Dilation

Scale Factor of a Dilation

Similar Polygons

Scale Factors of two similar polygons

A transformation in which the lines connecting every point, P…

The ration of lengths of the corresponding sides of image and…

Two similar polygons whose corresponding angles are congruent…

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

Dilation

A transformation in which the lines connecting every point, P…

Scale Factor of a Dilation

The ration of lengths of the corresponding sides of image and…

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.

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…

Midsegment

Midpoint

Perpendicular bisector

Equidistant

Connect the midpoints of two sides in a triangle. It is paral…

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

Connect the midpoints of two sides in a triangle. It is paral…

Midpoint

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

Polygon

Vertex

Diagonal

Regular polygon

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

The common endpoint at 2 sides

A segment that connects any 2 nonconsecutive vertices

One that is both equilateral and equiangular

Polygon

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

Vertex

The common endpoint at 2 sides

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 congruent parts (in half)

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

The same distance from the center point to the side

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 congruent parts (in half)

Two polygons

Statement proportionality

Scale factor

Perimeters of similar polygons (theorem)

are similar polygons if corresponding angels are congruent an…

they are ratios.

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 similar polygons if corresponding angels are congruent an…

Statement proportionality

they are ratios.

base

base angle

diagonal

isosceles trapezoid

parallel sides of a quadrilateral

formed by the base and one of the legs of a figure

a segment that connects any two nonconsecutive vertices

a trapezoid where the legs are congruent

base

parallel sides of a quadrilateral

base angle

formed by the base and one of the legs of a figure

Theorem 16

Definition of Line of Symmetry

Definition of Parallel

Equal Corresponding Angles Theorem

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

Two points are symmetric with respect to a line iff the line…

Two lines are parallel iff they lie in the same plane and do…

Equal corresponding angles mean that lines are parallel (If C…

Theorem 16

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

Definition of Line of Symmetry

Two points are symmetric with respect to a line iff the line…

foot of the line

four ways to determine a plane

how to prove a line not in the plane p…

what is the intersection of two planes

the point of intersection of a line that is not in the plane…

three noncolliner points, a line and a point not on the line,…

a line is perpendicular to a plane if it is perpendicular to…

a line

foot of the line

the point of intersection of a line that is not in the plane…

four ways to determine a plane

three noncolliner points, a line and a point not on the line,…

diagonal

Triangle

Quadrilateral

Pentagon

a segment that connects any two nonconsecutive vertices

number of sides 3... number of triangles 1... sum of interior angle…

number of sides 4... number of triangles 2... sum of interior angle…

number of sides 5... number of triangles 3... sum of interior angle…

diagonal

a segment that connects any two nonconsecutive vertices

Triangle

number of sides 3... number of triangles 1... sum of interior angle…

Incenter

median

circumcenter

centroid

the point of concurrency of the angle bisectors of a triangle

a segment from a vertex of a triangle to the midpoint of the…

the point of concurrency of the three perpendicular bisectors…

the point of concurrency of the three medians of a triangle

Incenter

the point of concurrency of the angle bisectors of a triangle

median

a segment from a vertex of a triangle to the midpoint of the…

Quadrilateral

Parallelogram

Rectangle

Rhombus

1.) 4 sides... 2.) lies in a plane

1.) 4 sides... 2.) lies in a plane... 3.) opposite sides parallel... 4…

1.) 4 sides... 2.) lies in a plane... 3.) opposite sides parallel... 4…

1.) 4 sides... 2.) lies in a plane... 3.) opposite sides parallel... 4…

Quadrilateral

1.) 4 sides... 2.) lies in a plane

Parallelogram

1.) 4 sides... 2.) lies in a plane... 3.) opposite sides parallel... 4…

Sides of a Polygon

Vertex of a Polygon

Diagonal

Regular Polygon

Each segment that forms a polygon.

The common endpoints of two sides.

A segment that connects any two nonconsecutive vertices.

Polygon that is both equilateral and equiangular.

Sides of a Polygon

Each segment that forms a polygon.

Vertex of a Polygon

The common endpoints of two sides.

Tangent circles

Arc-central angle

Chords-Arcs

Quartet of chords

Two circles that are tangent to the same line at the same point

The measure of an arc is the same as its central angle

If two chords in a circle are congruent, then their arcs are…

Congruent chords, congruent central angles, congruent arcs, c…

Tangent circles

Two circles that are tangent to the same line at the same point

Arc-central angle

The measure of an arc is the same as its central angle

Diagonal

Polygon Interior Angle Sum Theorem

Polygon Exterior Angle Sum Theorem

Parallelogram

In a polygon, a segment that connects nonconsecutive vertices…

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

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

A quadrilateral with parallel opposite sides. Any side of thi…

Diagonal

In a polygon, a segment that connects nonconsecutive vertices…

Polygon Interior Angle Sum Theorem

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

3 different ways to write ratios

Extended ratio

Proportion

Geometric mean

"a/b" or "a:b" or "a to b"

a ratio that compares two or more values

an equation that states two ratios are equal

a mean of two positive numbers that satisfies the equation as…

3 different ways to write ratios

"a/b" or "a:b" or "a to b"

Extended ratio

a ratio that compares two or more values

Equilateral polygon

Equiangular polygon

Regular Polygon

Parallelogram

A polygon with all sides congruent

A polygon with all angles congruent

A polygon that is both equilateral and equiangular

A quadrilateral with both pairs of opposite sides parallel

Equilateral polygon

A polygon with all sides congruent

Equiangular polygon

A polygon with all angles congruent

rational number

irrational number

Pythagorean theorem

sine

any whole number, fraction, mixed number or decimal; together…

a number without a predictable pattern of digits

in a right triangle, the sum of the squares of the lengths of…

the ratio of the leg opposite an acute angle to the hypotenuse

rational number

any whole number, fraction, mixed number or decimal; together…

irrational number

a number without a predictable pattern of digits

Vertex of a polygon

Diagonal

Regular polygon

Concave

common endpoint of two sides.

A segment that connects any 2 non-consecutive vertices.

Polygon with all congruent sides and angles.

Any part of a diagonal is outside the polygon.("caves in").

Vertex of a polygon

common endpoint of two sides.

Diagonal

A segment that connects any 2 non-consecutive vertices.

Rectangle

Kite

Consecutive Angles

Trapezoid

A _________ is a parallelogram with 4 Right Angles

A _________ is a quadrilateral with two pairs of adjacent sid…

Angles of a polygon that share a common side are _____________.

A __________ is a quadrilateral with exactly one pair of para…

Rectangle

A _________ is a parallelogram with 4 Right Angles

Kite

A _________ is a quadrilateral with two pairs of adjacent sid…

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 sonsecutive angles whose common side is a ba…

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

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 sonsecutive angles whose common side is a ba…

kite

trapezoid

isosceles trapezoid

parallelogram

a quadrilateral with 2 pairs of consecutive sides, but no opp…

a quadrilateral with exactly one pair of opposite sides paral…

a trapezoid with congruent legs, base angles are congruent, d…

a quadrilateral with opposite sides parallel, opposite sides…

kite

a quadrilateral with 2 pairs of consecutive sides, but no opp…

trapezoid

a quadrilateral with exactly one pair of opposite sides paral…

Sum of exterior angles always ='s

Formula for the number of triangles in…

To find how many sides something with…

Exterior Angles in a shape

360 degrees

Number of sides - 2

360/number given =Sides

Sum of exterior angles always ='s

360 degrees

Formula for the number of triangles in…

Number of sides - 2

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…

Midsegment

Midpoint

Perpendicular Bisector

Equidistant

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

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

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 two congruent sides (in h…

Tangent Conjecture

Tangent Segments Conjecture

Chord Central Angles Conjecture

Chord Arcs Conjecture

A tangent to a circle is perpendicular to the radius drawn to…

Tangent segments to a circle from a point outside the circle…

If two chords in a circle are congruent, then they determine…

If two chords in a circle are congruent, then their intercept…

Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to…

Tangent Segments Conjecture

Tangent segments to a circle from a point outside the circle…

Bases (trapezoid)

Base angles (trapezoid)

Diagonal

Isosceles trapezoid

The parallel sides of a trapezoid

The angles attached to the bases of a trapezoid

A segment connecting two non-consecutive vertices of a polygon

A trapezoid with congruent legs

Bases (trapezoid)

The parallel sides of a trapezoid

Base angles (trapezoid)

The angles attached to the bases of a trapezoid

Diagonal of a polygon

What is the formula for the sum of the…

What is the formula for finding one in…

What does the sum of the exterior angl…

A segment that connects any two nonconsecutive vertices

(n-2) x 180

(n-2)180 / n

360 degrees

Diagonal of a polygon

A segment that connects any two nonconsecutive vertices

What is the formula for the sum of the…

(n-2) x 180