# Study sets matching "honors theorems postulates geometry postulates theorems chap…"

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Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Same-side Interior Angle Postulate... If a…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a trans…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If a…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

Area Addition Postulate

Area of a Parallelogram

Area of a Triangle

Area of a Trapezoid

The area of a region is equal to the sum of the areas of its n…

A=bh

A=1/2bh

A=(b1+b2/2)h

Area Addition Postulate

The area of a region is equal to the sum of the areas of its n…

Area of a Parallelogram

A=bh

Through any two points there is exactly…

Through any three noncollinear points t…

If two points lie in a plane, then the…

If two lines intersect, they then inter…

Through any two points there is exactly one line

Through any three noncollinear points there is exactly one pla…

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

If two lines intersect, they then intersect at exactly one poi…

Through any two points there is exactly…

Through any two points there is exactly one line

Through any three noncollinear points t…

Through any three noncollinear points there is exactly one pla…

Chapter 9 - Tangents, Arcs & Chords

chord

secant

diameter

...

segment whose endpoints lie on a circle

a line that contains a chord

chord that contains center of circle

Chapter 9 - Tangents, Arcs & Chords

...

chord

segment whose endpoints lie on a circle

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponden…

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

Given line AB and a point O on line AB, all rays that can be d…

If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

Ruler Postulate

The points on a line can be put into a one-to-one corresponden…

Segment Addition Postulate

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

Pythagorean theorem

Pythagorean triple

converse of the Pythagorean theorem

Pythagorean inequalities theorem

in a right triangle, the square of the length of the hypotenus…

a set of three positive integers a, b, and c that satisfy the…

if the square of the length of the longest side of a triangle…

for any triangle, where c is the length of the longest side, i…

Pythagorean theorem

in a right triangle, the square of the length of the hypotenus…

Pythagorean triple

a set of three positive integers a, b, and c that satisfy the…

Theorem 6-1: The Exterior Angle Theorem

Theorem 6-2

Theorem 6-3

Corollary 1

The measure of an exterior angle of a triangle is greater than…

If one side of a triangle is longer than a second side, then t…

If one angle of a triangle is larger than a second angle, then…

The perpendicular segment from a point to a line is the shorte…

Theorem 6-1: The Exterior Angle Theorem

The measure of an exterior angle of a triangle is greater than…

Theorem 6-2

If one side of a triangle is longer than a second side, then t…

Theorem 7-1: SAS Similarity Theorem

Theorem 7-2: SSS Similarity Theorem

Theorem 7-3: Triangle Proportionality T…

Theorem 7-4: Triangle Angle-Bisector Th…

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

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

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

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

Theorem 7-1: SAS Similarity Theorem

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

Theorem 7-2: SSS Similarity Theorem

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

Theorem 9-1

Theorem 9-2

Theorem 9-3

Fundamental Theorem of Isometries

A translation or rotation is a composition of two reflections.

A composition of reflections across two parallel lines is a tr…

A composition of reflections across two intersecting lines is…

In a plane, one of two congruent figures can be mapped onto th…

Theorem 9-1

A translation or rotation is a composition of two reflections.

Theorem 9-2

A composition of reflections across two parallel lines is a tr…

composition of transformations

dilation

glide reflection

isometry/congruence transformation

a composition of two transformations is a transformation in wh…

a transformation created proportionally by enlarging or reduci…

the composition of a translation followed by a reflection acro…

a transformation in which an original figure and its image are…

composition of transformations

a composition of two transformations is a transformation in wh…

dilation

a transformation created proportionally by enlarging or reduci…

SSS Congruence Theorem

SAS Congruence Theorem

ASA Congruence Theorem

AAS Congruence Theorem

If the 3 sides of one triangle are congruent to the 3 sides of…

If 2 sides and the included angle of one triangle are congruen…

If 2 angles and the included side of one triangle are congruen…

If 2 angles and a non included side of one triangle are congru…

SSS Congruence Theorem

If the 3 sides of one triangle are congruent to the 3 sides of…

SAS Congruence Theorem

If 2 sides and the included angle of one triangle are congruen…

Postulates

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Statements that are accepted as true without proof

1. The points on a line can be paired with the real numbers in…

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

On AB in a given plane, choose any point O between A and B. Co…

Postulates

Statements that are accepted as true without proof

Ruler Postulate

1. The points on a line can be paired with the real numbers in…

AA Similarity

SSS Similarity

SAS Similarity

Triangle Proportionality theorem

If two angles of one triangle are ≅ to two angles of another t…

If the measures of the corresponding sides of two triangles ar…

If the measures of the two sides of a triangle are proportiona…

If a line is parallel to one side of a triangle and intersects…

AA Similarity

If two angles of one triangle are ≅ to two angles of another t…

SSS Similarity

If the measures of the corresponding sides of two triangles ar…

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

theorem 1

theorem 2

theorem 3

theorem 4

If two angles are right angles, then they are congruent

if two angles are straight angles, then they are congruent

If a conditional statement is true, the the contrapositive of…

If angles are supplementary to the same angle, then they are c…

theorem 1

If two angles are right angles, then they are congruent

theorem 2

if two angles are straight angles, then they are congruent

Largest Angle Theorem

Longest side theorem

Vertical angles theorem

Congruent supplements or complements th…

If two sides of a triangle are not congruent then the larger a…

if two angles of a triangle are not congruent then the longer…

vertical angles are congruent

if two angles are supplements or complements of the same angle…

Largest Angle Theorem

If two sides of a triangle are not congruent then the larger a…

Longest side theorem

if two angles of a triangle are not congruent then the longer…

Midpoint

Supplementary Angles

Perpendicular Lines

Congruent Angles

The point that divides, or bisects, a segment into two congrue…

Two angles whose measures have the sum of 180 degrees

Two lines that intersect to form a right angle

Angles that have the same measure

Midpoint

The point that divides, or bisects, a segment into two congrue…

Supplementary Angles

Two angles whose measures have the sum of 180 degrees

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Theorem 9-1

Theorem 9-2

Corollary

Postulate 16: Arc Addition Postulate

If a line is tangent to a circle, then the line is perpendicul…

If a line in the plane of a circle is perpendicular to a radiu…

Tangents to a circle from a point are congruent

The measure of the arc formed by two adjacent arcs is the sum…

Theorem 9-1

If a line is tangent to a circle, then the line is perpendicul…

Theorem 9-2

If a line in the plane of a circle is perpendicular to a radiu…

Midpoint definition

Segment bisector definition

Congruent segments definition

Angle addition postulate

A point that divides the segment into two congruent segments

a point, line, ray, or other segment that intersects a segment…

Segments that have the same length

Two little angles make one big angle

Midpoint definition

A point that divides the segment into two congruent segments

Segment bisector definition

a point, line, ray, or other segment that intersects a segment…

coplanar, do not intersect

equidistant

do not intersect

noncoplanar, do not intersect

Two lines are parallel iff they are ____ and __ ___ ____

Two lines are parallel iff they are everywhere ____

Two planes are parallel iff they _____ ____

Two lines are skew iff they are ____ and they __ ___ _____

coplanar, do not intersect

Two lines are parallel iff they are ____ and __ ___ ____

equidistant

Two lines are parallel iff they are everywhere ____

Unique Plane Theorem

Line-Plane Perpendicular Theorem

Point-Line-Plane Postulate (Expanded)

Unique Plane Assumption

There is exactly one plane through a line and a point not on t…

If a line is perpendicular to two different lines at their poi…

Contains the Unique Plane Assumption and Intersection Assumpti…

Through three non-collinear points, there is exactly one plane

Unique Plane Theorem

There is exactly one plane through a line and a point not on t…

Line-Plane Perpendicular Theorem

If a line is perpendicular to two different lines at their poi…