#### Study sets matching "geometry theorems etc"

#### Study sets matching "geometry theorems etc"

undefined term

point

line

plane

a word without a formal definition

undefined, a location with no size or dimension

undefined, a series of infinite points that extends in two di…

undefined, flat surface that has no thickness and extends in…

undefined term

a word without a formal definition

point

undefined, a location with no size or dimension

Segment Addition Postulate

Angle Addition Postulate

Midpoint

segment bisector

if b is between a and c, then ab+bc=ac

if point B lies in the interior of <AOC, then m<AOB +m<BOC=m<…

m is the midpoint of ab if and only if AM=MB

CD bisects AB if and only if M is the endpoint of AB

Segment Addition Postulate

if b is between a and c, then ab+bc=ac

Angle Addition Postulate

if point B lies in the interior of <AOC, then m<AOB +m<BOC=m<…

Postulate 1 (Ruler Postulate)

Postulate 2 (Segment Addition Postulate)

Postulate 3 (Protractor Postulate)

Postulate 4 (Angle Addition Postulate)

The distance between points a and b is the absolute value of…

If B is in between A and C, then AB+BC=AC

The measure of angle AOB is equal to the absolute value of th…

If point B is in the interior of angle COA, then the measure…

Postulate 1 (Ruler Postulate)

The distance between points a and b is the absolute value of…

Postulate 2 (Segment Addition Postulate)

If B is in between A and C, then AB+BC=AC

Bisection point

Midpoint

Trisect

Bisect

A point (or segment, ray, or line) that divides a segment int…

the bisection point of a segment

to divide a segment into 3 congruent segments (or angles)

to divide a segment into 2 congruent segments (or angles)

Bisection point

A point (or segment, ray, or line) that divides a segment int…

Midpoint

the bisection point of a segment

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a = b, then a + c = b + c

If a = b, then a - c = b - c

If a = b, then a * c = b * c

If a = b and c ≠ 0, then a/c = b/c

Addition Property of Equality

If a = b, then a + c = b + c

Subtraction Property of Equality

If a = b, then a - c = b - c

Addition property

Subtraction property

Multiplication property

Division property

If A=B and C=D, then a+c=b+d

If A=B and C=D, then a-c=b-d

If A=B, then CA=CB

If A=B, then C=0, then a/c=b/c

Addition property

If A=B and C=D, then a+c=b+d

Subtraction property

If A=B and C=D, then a-c=b-d

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

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

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two triangles are in proportion, then the tri…

If a line parallel to one side of a triangle intersects the o…

AA Similarity Postulate

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

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…

isosceles triangle theorem

isosceles triangle converse

1 corollary

2 corollary

if two sides are congruent then the angles opp. the sides are…

if two angles are congruent then the sides opp. those angles…

the acute angles of a right triangle are comp.

the measure of each angle of equiangular triangle is 60 degre…

isosceles triangle theorem

if two sides are congruent then the angles opp. the sides are…

isosceles triangle converse

if two angles are congruent then the sides opp. those angles…

perpendicular lines

skew lines

Parallel planes

transversal

intersect at 90 degree angles

are not coplanar, parallel, and do not intersect

planes that do not intersect

a line that intersects to coplanar lines at two different poi…

perpendicular lines

intersect at 90 degree angles

skew lines

are not coplanar, parallel, and do not intersect

Posulate 5

Poatulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line.

A line contains at least two points.

If two lines intersect, then their intersection is exactly on…

Through any three noncollinear points there exists exactly on…

Posulate 5

Through any two points there exists exactly one line.

Poatulate 6

A line contains at least two points.

Same-Side Interiors Angle Postulate

Alternate Interior Angles Theorem

Corresponding Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then same-sid…

If a transversal intersects two parallel lines, the alternate…

If a transversal intersects two parallel lines, then correspo…

If a transversal intersects two parallel lines, then alternat…

Same-Side Interiors Angle Postulate

If a transversal intersects two parallel lines, then same-sid…

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, the alternate…

Linear Pair Theorem

Theorem

Congruent supplements theorem

Right angle congruence theorem

If 2 angles form a linear pair, then they are supplementary

A statement that must be proven

If 2 angles are supplementary to the same angle, then the 2 a…

All right angles are congruent

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Theorem

A statement that must be proven

Point

Name Points

Line

Name Lines

A location in space that has no dimension

Upper-case print letter is used to __.

A set of infinite points in one dimension;goes infinitely in…

Using a lower-case cursive letter OR using a 2 points and a l…

Point

A location in space that has no dimension

Name Points

Upper-case print letter is used to __.

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

point, line, plane

collinear points

axioms

theorems

the three undefined terms in geometry

points on the same line

statements that are accepted without proofs

statements that can be proven

point, line, plane

the three undefined terms in geometry

collinear points

points on the same line

Definition of parallel lines

Definition of skew lines

Definition of parallel planes

If two parallel planes are cut by a th…

Coplanar lines that do not intersect

Noncoplanar lines; neither parallel or intersecting

Non intersecting planes

The lines of intersection are parallel

Definition of parallel lines

Coplanar lines that do not intersect

Definition of skew lines

Noncoplanar lines; neither parallel or intersecting

If a = b and c = d, then a+c = b+d.

If a = b and c = d, then a-c = b-d.

If M is the midpoint of AB, then AM =…

If AD is the bisector of <CAB then m<B…

Addition Property:

Subtraction Property:

Theorum 2-1: Midpoint Theorem

Theorum 2-2: Angle Bisector Theorem.

If a = b and c = d, then a+c = b+d.

Addition Property:

If a = b and c = d, then a-c = b-d.

Subtraction Property:

cpctc

SSS postulate

sas postulate

asa postulate

Corresponding parts of congruent triangles are congruent

If three sides of one triangle are congruent to three sides o…

If two sides and the included angle of one triangle are congr…

If two angles and the included side of one of triangle are co…

cpctc

Corresponding parts of congruent triangles are congruent

SSS postulate

If three sides of one triangle are congruent to three sides o…

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

If a=b and c=d, then a+c=b+d

If a=b and c=d, then a-c=b-d

If a=b, then ca=cb

If a=b and c≠0, then a÷c=b÷c

Addition Property of Equality

If a=b and c=d, then a+c=b+d

Subtraction Property of Equality

If a=b and c=d, then a-c=b-d

Linear Pair Theorem

Theorem

Congruent supplements theorem

Right angle congruence theorem

If 2 angles form a linear pair, then they are supplementary

A statement that must be proven

If 2 angles are supplementary to the same angle, then the 2 a…

All right angles are congruent

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Theorem

A statement that must be proven

Definition of Midpoint

Definition of Bisector

Angle Addition Postulate

Addition Prop. of =

a point that divides a segment into two congruent segments

a line, segment, or ray that intersects a line segment at its…

if point B lies in the interior of <AOC then <AOB + <BOC=<AOC…

if a=b and c=d then a+c=b+d

Definition of Midpoint

a point that divides a segment into two congruent segments

Definition of Bisector

a line, segment, or ray that intersects a line segment at its…

Linear Pair Theorem

Theorem

Congruent supplements theorem

Right angle congruence theorem

If 2 angles form a linear pair, then they are supplementary

A statement that must be proven

If 2 angles are supplementary to the same angle, then the 2 a…

All right angles are congruent

Linear Pair Theorem

If 2 angles form a linear pair, then they are supplementary

Theorem

A statement that must be proven

A point (or segment, ray, or line) tha…

two points at which the segment is div…

A ray that divides an angle into two c…

Dividing ray is called the

Bisects the Midpoint

trisection points

bisects

angle bisector

A point (or segment, ray, or line) tha…

Bisects the Midpoint

two points at which the segment is div…

trisection points

Reflexive Property of Equality (Refl.…

Symmetric Property of Equality (Symm.…

Transitive Property of Equality (Trans…

Substitution Property of Equality (Sub…

a=a

If a=b, the b=a

If a=b and b=c, the a=c

If a=b, then a may be replaced by b in any equation or expres…

Reflexive Property of Equality (Refl.…

a=a

Symmetric Property of Equality (Symm.…

If a=b, the b=a

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

the exterior angle inequality theorem…

converse (pg.208)

inverse (pg.208)

contrapositive (pg.208)

the measure of an exterior angle of a triangle is greater tha…

if q, then p... (if the original statement is: if p, then q)

if not p, then not q ... (if the given statement is: if p, then q)

if not q, then not p... (if the given statement is: if p, then q)

the exterior angle inequality theorem…

the measure of an exterior angle of a triangle is greater tha…

converse (pg.208)

if q, then p... (if the original statement is: if p, then q)

line

collinear

axioms/postulates

theorems

made up of points and has no thickness or width (undefined te…

points on the same line

statements that are accepted WITHOUT proofs

statements that can be proven

line

made up of points and has no thickness or width (undefined te…

collinear

points on the same line

postulate

Segment Addition Postulate

acute angles

obtuse angles

an accepted statement of fact without proog

If B is between A and C then AB+BC=AC

measure between 0 and 90 degrees

measure between 90 and 180

postulate

an accepted statement of fact without proog

Segment Addition Postulate

If B is between A and C then AB+BC=AC

Midpoint theorem

Angle bisector theorem

Vertical angle theorem

Perpendicular adjacent angle theorem

If M is the midpoint of line AB, then AM= 1/2AB and MB=1/2AB

If ray BX is the bisector of angle ABC, then the measurement…

Virgil s angles are congruent

If two lines are perpendicular, then they form congruent adja…

Midpoint theorem

If M is the midpoint of line AB, then AM= 1/2AB and MB=1/2AB

Angle bisector theorem

If ray BX is the bisector of angle ABC, then the measurement…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Through any two points there exists exactly one line.

A line contains at least two points.

If two lines intersect, then their intersection is exactly on…

Throught any three noncollinear points there exists exactly o…

Postulate 5

Through any two points there exists exactly one line.

Postulate 6

A line contains at least two points.

Theorem

Theorem

Theorem

5 ways to prove quadrilaterals are con…

Opposite sides of a parallelogram are congruent

Opposite angles of a parallelogram are congruent

Diagonals of a parallelogram bisect each other

1. Show that both pairs of opposite sides are parallel ... 2. Sh…

Theorem

Opposite sides of a parallelogram are congruent

Theorem

Opposite angles of a parallelogram are congruent

squares of the legs

Pythagorean Theorem

Right Triangle

½(b)(h)

Pythagorean Theorem: In a right triangle, the square of the l…

What theorem is this?

The Pythagorean Theorem is only true for what type of triangle?

Area of a triangle

squares of the legs

Pythagorean Theorem: In a right triangle, the square of the l…

Pythagorean Theorem

What theorem is this?

congruent; proportional

scale factor

scale factor

scale factor

In similar polygons, corresponding angles are __________, cor…

If 2 polygons are similar, the ratio of the lengths is 2 corr…

The ration lengths in similar polygons is the same as the ___…

The ratio of the perimeter is similar polygons is the same as…

congruent; proportional

In similar polygons, corresponding angles are __________, cor…

scale factor

If 2 polygons are similar, the ratio of the lengths is 2 corr…

Midsegment of a Triangle

Parallel; the third side half; the thi…

Midsegment Theorem

Midpoint formula

A segment that connects the midpoints of 2 sides of the trian…

Midsegment Theorem: The segment connecting the midpoints of 2…

What theorem?

What formula is this?

Midsegment of a Triangle

A segment that connects the midpoints of 2 sides of the trian…

Parallel; the third side half; the thi…

Midsegment Theorem: The segment connecting the midpoints of 2…

Point

Line

Plane

Collinear

has no size, represented by a dot

extends indefinitely and has no thickness or width; named by…

has two dimensions; represented by a shape that looks like a…

points that lie on the same line

Point

has no size, represented by a dot

Line

extends indefinitely and has no thickness or width; named by…

A circle is a set of all points in a p…

A radius is the distance from the cent…

A chord is a segment whose endpoints a…

A diameter is a chord that..

equidistant

any point on the circle

opposite sides of the circle

contains the center of the circle

A circle is a set of all points in a p…

equidistant

A radius is the distance from the cent…

any point on the circle

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

What is a diagonal?

Polygon Interior Angles Theorem: The s…

Interior Angles of a Quadrilateral: Th…

What is a quadrilateral?

segment that joins 2 nonconsecutive vertices

"n" is the number of sides the figure has.

360 degrees

4 sided figure

What is a diagonal?

segment that joins 2 nonconsecutive vertices

Polygon Interior Angles Theorem: The s…

"n" is the number of sides the figure has.

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

point

plane

line

collinear points

a location (undefined term)

a flat surface made up of points; has no depth and extends in…

made up of points and has no thickness or width (undefined te…

points on the same line

point

a location (undefined term)

plane

a flat surface made up of points; has no depth and extends in…

Midsegment of a triangle

How many midsegments does a triangle h…

Midsegment Theorem

A segment, ray, line, or plane that is…

a segment that connects the midpoints of two sides of the tri…

3

The segment connecting the midpoints of two sides of a triang…

Perpendicular bisector

Midsegment of a triangle

a segment that connects the midpoints of two sides of the tri…

How many midsegments does a triangle h…

3

Conditional Statement

Hypothesis

Conclusion

Converse of a conditional statement

A type of logical statement that has two parts, a hypothesis…

The if part of a conditional statement.

The then part of a conditional statement

The statement formed by switching the hypothesis and conclusi…

Conditional Statement

A type of logical statement that has two parts, a hypothesis…

Hypothesis

The if part of a conditional statement.

Definition of a line

Definition of a plane

Definition of a plane

Definition of line intersection

Through any two points there is exactly one line.

Through any three noncollinear points there is exactly one pl…

If two points lie in a plane, then the line containing the po…

If two lines intersect they intersect at exactly one point.

Definition of a line

Through any two points there is exactly one line.

Definition of a plane

Through any three noncollinear points there is exactly one pl…

Perpendicular Transversal converse

Alternate Interior Angles Converse The…

Alternate Exterior Angles Converse The…

Converse of Corresponding Angles Postu…

If two lines are perpendicular to the same line, then those t…

If alternate interior angles are congruent, then the lines ar…

Alternate exterior angles that are congruent implies parallel…

If corresponding angles are congruent, then the lines are par…

Perpendicular Transversal converse

If two lines are perpendicular to the same line, then those t…

Alternate Interior Angles Converse The…

If alternate interior angles are congruent, then the lines ar…

Adjacent angles

Corresponding angles

Alternate interior angles

Alternate exterior angles

A pair of angles that share a common side

are congruent when two lines are parallel to one another and…

The angles that are on opposite sides of the transversal and…

The angles that are on oppostie sides of the transversal and…

Adjacent angles

A pair of angles that share a common side

Corresponding angles

are congruent when two lines are parallel to one another and…