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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

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.

Coplanar

Non Coplanar

What does determine mean?

How can you determine a plane?

two or more points, lines, or rays that are on the same plane

3 or more points that are not all on the same plane

determine means there is one and only one

three noncollinear points determine a plane, a line and a poi…

Coplanar

two or more points, lines, or rays that are on the same plane

Non Coplanar

3 or more points that are not all on the same plane

parallelogram

rhombus

rectangle

square

quadrilateral with 2 pairs of opposite sides parallel

a parallelogram with all sides congruent

parallelogram with 4 right angles

rectangle with 4 congruent sides

parallelogram

quadrilateral with 2 pairs of opposite sides parallel

rhombus

a parallelogram with all sides congruent

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

Diagonal

Polygon Interior Angle Theorem

Regular Polygon Interior Angle Theorem

Polygon Exterior Angle Theorem

connects any 2 nonconsecutive vertices

the sum of the measures of the interior angles of a polygon i…

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

the sum of one exterior angle per vertex of any polygon is 360

Diagonal

connects any 2 nonconsecutive vertices

Polygon Interior Angle Theorem

the sum of the measures of the interior angles of a polygon i…

polygon

sides

vertex

diagonal

a plane figure that is formed by three or more segments

a polygon is formed by three or more segments called

in a polygon, each endpoint is a

a segment that joins two nonconsecutive vertices of a polygon…

polygon

a plane figure that is formed by three or more segments

sides

a polygon is formed by three or more segments called

Flip-Flop Theorem 6-1

Segment Symmetry Theorem 6-1

Side-Switching Theorem 6-1

Angle Symmetry Theorem 6-1

If F and G are points / figures and rL(F) = G, then rL(G) = F

Every segment has exactly two symmetry lines:... 1) the line of…

If one side of an angle is reflected over the line containing…

The line containing the bisector of an angle is a symmetry li…

Flip-Flop Theorem 6-1

If F and G are points / figures and rL(F) = G, then rL(G) = F

Segment Symmetry Theorem 6-1

Every segment has exactly two symmetry lines:... 1) the line of…

Polygon Angle Sum Theorem

Polygon Exterior angles sum theorem

Properties of Parallelograms (6-2-1)

Properties of Parallelograms (6-2-2)

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

The sum of the exterior angle measures, one angle at each ver…

if a quadrilateral is a parallelogram, then its opposite side…

If a quadrilateral is a parallelogram, then its opposite angl…

Polygon Angle Sum Theorem

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

Polygon Exterior angles sum theorem

The sum of the exterior angle measures, one angle at each ver…

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…

when any part of a diagonal contains points in the exterior o…

when no diagonal contains points in the exterior of the polygon

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…

similar triangles

Angle-Angle Similarity Theorem

Side-Side Similarity Theorem

included angle

triangles that have all pairs of corresponding angles congrue…

"If two angles of one triangle are congruent to two angles of…

"If all three corresponding sides of two triangles are propor…

an angle formed by two consecutive sides of a figure

similar triangles

triangles that have all pairs of corresponding angles congrue…

Angle-Angle Similarity Theorem

"If two angles of one triangle are congruent to two angles of…

Altitude of a triangle

Median of a triangle

congruent.

equiangular

A segment drawn from any vertex of the triangle perpendicular…

A segment drawn from any vertex of the triangle to the midpoi…

Base Angle Theorem - If two sides of a triangle are congruent…

If a triangle is equilateral, then it is also ____

Altitude of a triangle

A segment drawn from any vertex of the triangle perpendicular…

Median of a triangle

A segment drawn from any vertex of the triangle to the midpoi…

6.1 Definition of A parallelogram

Theorem 6.2

Theorem 6.3

Theorem 6.4

A quadrilateral where both pairs of opposite sides are parallel

If a quadrilateral is a parallelogram

If a quadrilateral is a paralleogram, then it's opposite angl…

If a quadrilateral is a parallelogram, then its consecutive a…

6.1 Definition of A parallelogram

A quadrilateral where both pairs of opposite sides are parallel

Theorem 6.2

If a quadrilateral is a parallelogram

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

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…

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.

polygon

diagonal

regular polygon

concave polygon

a closed plane figure formed by 3 or more line segments that…

a segment that connects any 2 nonconsecutive vertices in a po…

a polygon that is both equilateral and equiangular

a polygon is considered concave if any part of a diagonal con…

polygon

a closed plane figure formed by 3 or more line segments that…

diagonal

a segment that connects any 2 nonconsecutive vertices in a po…

scale drawing

scale

dialation

center of dialation

same shape as the object the scale represents

relation of the dimensions in the drawing compared to the act…

transformation that stretches or shrinks a figure to create a…

ratio of a side length of the image to the corresponding side…

scale drawing

same shape as the object the scale represents

scale

relation of the dimensions in the drawing compared to the act…

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…

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

1st Property of Inequality... If a>b and…

2nd property of inequality... If a>b and…

3rd property of inequality... If a>b and…

4th property of inequality... If a>b and…

then a+c>b+d

then ac>bc and a/c>b/c

then ac<bc and a/c<b/c

then a>c

1st Property of Inequality... If a>b and…

then a+c>b+d

2nd property of inequality... If a>b and…

then ac>bc and a/c>b/c

Chord Central Angles Conjecture

Chord Arcs Conjecture

Perpendicular to a Chord Conjecture

Chord Distance to Center Conjecture

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

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

The perpendicular from the center of a circle to a chord is t…

Two congruent chords in a circle are equidistant from the cen…

Chord Central Angles Conjecture

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

Chord Arcs Conjecture

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

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…

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

Perimeters of similar polygons

Angle-angle similarity postulate

Side-side-side similarity theorem

Side-angle-side similarity theorem

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

If two angles of one triangle are congruent to two angles of…

If the corresponding side lengths of two triangles are propor…

If an angle of one triangle is congruent to an angle of a sec…

Perimeters of similar polygons

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

Angle-angle similarity postulate

If two angles of one triangle are congruent to two angles of…

polygon

sides of a polygon

vertex of a polygon

diagonal of a polygon

A closed plane figure formed by three or more line segments

Each line segment that forms a polygon

the point where two sides of a polygon meet

A segment that joins 2 nonconsecutive vertices of a polygon

polygon

A closed plane figure formed by three or more line segments

sides of a polygon

Each line segment that forms a polygon

Dilation

Scale factor of a Dilation

Similar Polygons

Scale Factor of Two Similar Polygons

A transformation in which the lines connecting every point P…

In a Dilation, the ratio of a linear measurement of the image…

Two polygons whose corresponding angles are congruent and who…

All corresponding sides and angles in a triangle are congruent.

Dilation

A transformation in which the lines connecting every point P…

Scale factor of a Dilation

In a Dilation, the ratio of a linear measurement of the image…

Opposite Sides are Parallel

Opposite Sides are Congruent

Opposite Angles are Congruent

Diagonals Bisect Each Other

Parallelogram, rectangle, rhombus, square

Parallelogram, rectangle, rhombus, square

Parallelogram, rectangle, rhombus, square

Parallelogram, rectangle, rhombus, square

Opposite Sides are Parallel

Parallelogram, rectangle, rhombus, square

Opposite Sides are Congruent

Parallelogram, rectangle, rhombus, square

Rhombus

Rectangle

Square

Trapezoid

Has all properties of a parallelogram, four congruent sides,…

Parallelogram with four right angles, diagonals are congruent

A parallelogram with four congruent sides and four right angl…

A quad with one pair of parallel sides

Rhombus

Has all properties of a parallelogram, four congruent sides,…

Rectangle

Parallelogram with four right angles, diagonals are congruent

theorem 6-1

theorem 6-2

theorem 6-3

theorem 6-4

opposite sides of a parallelogram are congruent

opposite angles of a parallelogram are congruent

the diagonals of a parallelogram bisect each other

if three (or more) parallel lines cut off congruent segments…

theorem 6-1

opposite sides of a parallelogram are congruent

theorem 6-2

opposite angles of a parallelogram are congruent

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.

Circumcenter

Incenter

Centroid

Orthocenter

Point of concurrency equidistant from the 3 vertices of a tri…

Point of concurrency equidistant from the sides of a triangle…

Point of concurrency that is 2/3 the distance from each verte…

Point of concurrency, made by concurrent altitudes.

Circumcenter

Point of concurrency equidistant from the 3 vertices of a tri…

Incenter

Point of concurrency equidistant from the sides of a triangle…

similar polygons

statement of proportionality

scale factor

perimeters of similar polygons theorem

two polygons are this if corresponding angles are congruent a…

AB/DE = BC/EF = CA/FD

the ratio of the lengths of two corresponding sides if two po…

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

similar polygons

two polygons are this if corresponding angles are congruent a…

statement of proportionality

AB/DE = BC/EF = CA/FD

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…

What are concurrent line?

What is an angle bisector?

What if the point of concurrency of an…

The incenter is the center of what?

3 or more lines that intersect at one point

a line that bisects an angle

incenter

an inscribed circle

What are concurrent line?

3 or more lines that intersect at one point

What is an angle bisector?

a line that bisects an angle

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…

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Angle Bisector Theorem

Converse of the Angle Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

In a plane, if a point is equidistant from the endpoints of…

If a point lies on the bisector of an angle, then it is ... equi…

If a point is in the interior of an angle and is equidistant…

Perpendicular Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

Converse of the Perpendicular Bisector…

In a plane, if a point is equidistant from the endpoints of…

Concave

Diagonal

Isosceles Trapezoid

Kite

Exterior of a polygon

Segment that connects any two nonconsecutive verticles

Legs of a trapezoid are congruent

Quadrilateral with two pairs of congruent consecutive sides

Concave

Exterior of a polygon

Diagonal

Segment that connects any two nonconsecutive verticles

ratio of a to b

proportion

geometric mean

scale drawing

a comparison of 2 numbers using division.

an equation that states that two ratios are equal

for two positive numbers a and b, the positive number x that…

a drawing that is the same shape as the object it represents

ratio of a to b

a comparison of 2 numbers using division.

proportion

an equation that states that two ratios are equal

rectangle definition

Rhombus definition

square definition

If a parallelogram is a rhombus, then…

a parallelogram with 4 right angles

a parallelogram with all sides congruent ... " squished square"

a parallelogram with 4 right angles and all sides congruent.…

the diagonals are perpendicular to each other.

rectangle definition

a parallelogram with 4 right angles

Rhombus definition

a parallelogram with all sides congruent ... " squished square"

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…

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