# Study sets matching "honors theorems postulates geometry postulates theorems chapter 9"

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

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

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…

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

Theorem 9-1

Corollary to Theorem 9-1

Theorem 9-2 (converse of theorem 9-1)

Arc Addition Postulate

If a line is tangent to a circle, then it is perpendicular to…

Tangent segments to a circle from an external point are congru…

If a line is perpendicular to a radius at its outer endpoint,…

One arc plus another arc will equal the total value of the two…

Theorem 9-1

If a line is tangent to a circle, then it is perpendicular to…

Corollary to Theorem 9-1

Tangent segments to a circle from an external point are congru…

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

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 paired with the real numbers in su…

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

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of angle AOC, then the measure…

Ruler Postulate

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

Segment Addition Postulate

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

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…

Postulate 5

Postulate 6

Postulate 7

Postulate 8

(1) A line contains at least two points (2) A plane contains a…

Through any two points there is exactly one line.

(1) Through any three points there is at least one plane (2) T…

If two points are in a plane, then the line that contains the…

Postulate 5

(1) A line contains at least two points (2) A plane contains a…

Postulate 6

Through any two points there is exactly one line.

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…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be matched one to one with real numbe…

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

Consider OB and a point A on one side of OB. The rays of the f…

If P is the interior of angleRST, then the measure of angleRSP…

Ruler Postulate

The points on a line can be matched one to one with real numbe…

Segment Addition Postulate

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

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

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, then they intersect in exactly one poi…

Postulate 1-1-1

Through any two points there is exactly one line

Postulate 1-1-2

Through any three noncollinear points there is exactly one pla…

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…

Postulate 1-1-1

Postulate 1-1-2

Postulate 1-1-3

Postulate 1-1-4

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, then they intersect at exactly one poi…

Postulate 1-1-1

Through any two points there is exactly one line.

Postulate 1-1-2

Through any three noncollinear points there is exactly one pla…

2 point, 1 line postulate

3 nonconllinear points, 1 plane postula…

segment addition postulate

angle addition postulate

through any two points, there exists only one line

through any three points not on one line, there exists only on…

AB+BC=AC... if AB+BC=AC, then B lies between A and C

m angle XYZ= m angle XYW+ m angle WYZ

2 point, 1 line postulate

through any two points, there exists only one line

3 nonconllinear points, 1 plane postula…

through any three points not on one line, there exists only on…

postulate 1-1

postulate 1-2

postulate 1-3

postulate 1-4

through any 2 points there is exactly 1 line

if 2 distinct lines intersect, then they intersect in exactly…

if 2 distinct planes intersect, then they intersect in exactly…

through any three non-collinear points there is exactly 1 plane

postulate 1-1

through any 2 points there is exactly 1 line

postulate 1-2

if 2 distinct lines intersect, then they intersect in exactly…

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…

Segment Addition Postulate

Angle Addition Postulate

Two Point Postulate

Line-Point Postulate

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

If P is in the interior of angle RST, then the measure of angl…

Through any two points, there exists exactly one line.

A line contains at least two points.

Segment Addition Postulate

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

Angle Addition Postulate

If P is in the interior of angle RST, then the measure of angl…

If two angles are supplementary to the…

If two angles form a linear pair, then…

If two angles are complementary to the…

All right angles are congurent

Congruent Supplements Theorem

Linear Pair Theorem

Congruent Complements Theorem

Right Angle Congruence Theorem

If two angles are supplementary to the…

Congruent Supplements Theorem

If two angles form a linear pair, then…

Linear Pair Theorem

Complementary Angles

Congruent Angles

Congruent Complements Theorem

Congruent Segments

Two angles whose measures have the sum of 90 degrees.

Angles that have the same measure.

If two angles are complementary to the same angle or to congru…

Segments that have the same length.

Complementary Angles

Two angles whose measures have the sum of 90 degrees.

Congruent Angles

Angles that have the same measure.

Tangent Theorem

Converse of the Tangent Theorem

Tangent Segments Theorem

Chords and Arcs Theorem

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

If a line is perpendicular to a radius of a circle at its endp…

If 2 segments are tangent to a circle from the same external p…

Congruent chords intercept congruent arcs in a circle or in co…

Tangent Theorem

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

Converse of the Tangent Theorem

If a line is perpendicular to a radius of a circle at its endp…

Congruent Circles Theorem

Similar Circles Theorem

Tangent Segments Theorem

Secant Segments Theorem

Two or more circles are congruent if they have the same radius…

All circles are similar

If two tangents intersect outside of a circle, they are congru…

If two secants intersect outside of a circle, then the product…

Congruent Circles Theorem

Two or more circles are congruent if they have the same radius…

Similar Circles Theorem

All circles are similar

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

Through any two points there is exactly one line.

If two distinct lines intersect, then they intersect in exactl…

If two distinct planes intersect, then they intersect in exact…

Through any three non-collinear points there is exactly one pl…

Postulate 1-1

Through any two points there is exactly one line.

Postulate 1-2

If two distinct lines intersect, then they intersect in exactl…