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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

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…

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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

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…

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 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…

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…

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

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 ____

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

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

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…

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

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…

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 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…

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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 ab=bc

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

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…

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

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.