# Study sets matching "geometry theorems postulates"

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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 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

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

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

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

Given ray OB, all rays OA forming angle BOA can be matched one…

If point B lies in the interior of angle AOC, then m∠AOB + m∠B…

Ruler Postulate

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

Segment Addition Postulate

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

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 non collinear points there is exactly one plane co…

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

If two lines intersect, then they intersect in exactly one pla…

Postulate 1-1-1

Through any two points there is exactly one line.

Postulate 1-1-2

Through any non collinear points there is exactly one plane co…

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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 exactly…

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

Through any 3 noncollinear points there is exactly one plane

Postulate 1-1

Through any two points there is exactly one line

Postulate 1-2

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

P1: The points on a line can be matched…

P2: If B is between A and C, then AB+BC…

P3: Consider ray OB and a point A on on…

P4: If P is in the interior of angle RS…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

P1: The points on a line can be matched…

Ruler Postulate

P2: If B is between A and C, then AB+BC…

Segment Addition Postulate

composite figure

circumference (definition)

circumference of a circle

arc length (definition)

a figure that consists of triangles, squares, rectangles, and…

the distance around a circle

the circumference C of a circle is C = πd or C = 2πr, where d…

a portion of the circumference of a circle

composite figure

a figure that consists of triangles, squares, rectangles, and…

circumference (definition)

the distance around a circle

If lines parallel then...

if corresponding angles are congruent

if same side angles are supplementary

if alt int/ext are congruent

same side angles are supplementary... corresponding angles are co…

lines are parallel

then lines are parallel

then lines parallel

If lines parallel then...

same side angles are supplementary... corresponding angles are co…

if corresponding angles are congruent

lines are parallel

Addition Property

Subtraction Property

Substitution

Segment and Angle Addition

If equal quantities are added to equal quantities, their sums…

If equal quantities are subtracted from equal quantities, thei…

Any quantity may be substituted for its equal

The whole is equal to the sum of its parts

Addition Property

If equal quantities are added to equal quantities, their sums…

Subtraction Property

If equal quantities are subtracted from equal quantities, thei…

Same side interior angles postulate

Alternate Interior Angle Postulate

Corresponding Angles Theorem.

Alternate Exterior Angles theorem

if a transversal intersects 2 parallel lines, then same side i…

if a transversal intersects two parallel lines, then alternate…

if a transversal intersects 2 parallel lines, then correspondi…

if a transversal intersects 2 parallel lines, then alternate e…

Same side interior angles postulate

if a transversal intersects 2 parallel lines, then same side i…

Alternate Interior Angle Postulate

if a transversal intersects two parallel lines, then alternate…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

A line can be drawn through any two points

A segment can be extended indefinitely to form a straight line

A circle is determined by a center point and a fixed distance…

All right angles are congruent

Postulate 1

A line can be drawn through any two points

Postulate 2

A segment can be extended indefinitely to form a straight line

side XY is congruent to side XZ

Triangle Sum Thm.

Isosceles Triangle Thm.

two congruent sides

Since XY equals XZ

M<X + M<Y + M<Z = 180

base angles Z & Y are congruent so m<Z = M<Y

Isosceles Triangles have at least

side XY is congruent to side XZ

Since XY equals XZ

Triangle Sum Thm.

M<X + M<Y + M<Z = 180

intersecting line theorem

hypotenuse leg theorem

Side-Side-Side (SSS) postulate

Side-Angle-Side (SAS) postulate

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

If two right triangles have congruent hypotenuses and correspo…

If the sides of one triangle are congruent to the sides of a s…

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

intersecting line theorem

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

hypotenuse leg theorem

If two right triangles have congruent hypotenuses and correspo…

if 2 lines are cut by a transversal so…

if given a line and a point not on the…

if 2 lines in a plane are cut by a tran…

if 2 lines in a plane are cut by a tran…

postulate 3.4 (converse of corresponding angles)

postulate 3.5 (parallel postulate)

theorem 3.5 (alternate exterior)

theorem 3.6 (consecutive interior)

if 2 lines are cut by a transversal so…

postulate 3.4 (converse of corresponding angles)

if given a line and a point not on the…

postulate 3.5 (parallel postulate)

Right Angle Congruence Theorem

Congruent Supplement Theorem

Congruent Complement Theorem

Vertical Angle Theorem

States "All right angles are congruent"

States "If two angles are supplements of the same angle or of…

States "If two angles are complements of the same angle or of…

States "Vertical angles are congruent"

Right Angle Congruence Theorem

States "All right angles are congruent"

Congruent Supplement Theorem

States "If two angles are supplements of the same angle or of…

they are congruent.... Right Angles Congr…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Suppleme…

they are congruent.... Congruent Compleme…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Congr…

If two angles are right angles, then

they are congruent.... Congruent Suppleme…

If two angles are supplementary to the same angle, then

Parallel Postulate

Perpendicular Postulate

Two Lines Perpendicular to a Third Line

Alternate Interior Angles Theorem

Through a point not on a line, there is one and only one line…

Through a point not on a line, there is one and only one line…

In a plane, if two lines are perpendicular to the same line th…

If two lines and a transversal form alternate interior angles…

Parallel Postulate

Through a point not on a line, there is one and only one line…

Perpendicular Postulate

Through a point not on a line, there is one and only one line…

Theorem 1-1

Theorem 1-2

Theorem 1-3

Complimentary Angles

If 2 lines intersect, then they intersect in exactly 1 point

Through a line and a point not in the line, there is exactly o…

If 2 lines intersect, then exactly 1 plane contains the lines

2 angles whose measures have a sum of 90 degrees

Theorem 1-1

If 2 lines intersect, then they intersect in exactly 1 point

Theorem 1-2

Through a line and a point not in the line, there is exactly o…

Segment addition postulate

Angle addition postulate

Through any two points

Through any three points there is at le…

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

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

Through any two points there is exactly one line

Through any three points there is at least one plane, and thro…

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 angle AOC, then measurement…

segment addition postulate (1.2)

midpoint (1.3)

segment bisector (1.3)

angle addition postulate (1.5)

when 3 points are collinear, you can say that one point is bet…

midpoint of a segment is the point that divides the segment in…

point, ray line, line segment or plane that intersects the seg…

if angle AB is equal to angle BC, then angle AB + angle BC = AC

segment addition postulate (1.2)

when 3 points are collinear, you can say that one point is bet…

midpoint (1.3)

midpoint of a segment is the point that divides the segment in…

Vertical Angles Theorem

Linear Pair Theorem

Same-Side Interior Angle Postulate

Alternate Interior Angles Theorem

If two angles are vertical angles, then they are congruent.

If two angles form a linear pair, then they are supplementary.

If two parallel lines are cut by a traversal, then the pairs o…

If two parallel lines are cut by a transversal, then the alter…

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent.

Linear Pair Theorem

If two angles form a linear pair, then they are supplementary.

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segment addition postulate

angle addition postulate

linear pair theorem

congruent supplements theorem

If a point (c) is between two points (a and b), then ac+cb= ab.

If a point (d) is in the interior of angle <ABC, then <ABD + <…

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

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

segment addition postulate

If a point (c) is between two points (a and b), then ac+cb= ab.

angle addition postulate

If a point (d) is in the interior of angle <ABC, then <ABD + <…

something you know to be true and is ac…

a statement that can be proven

if B is between A and C, then AB + BC =…

m<AOB + m<BOC = m<AOC

what is a postulate?

what is a theorem?

segment addition postulate

angle addition postulate

something you know to be true and is ac…

what is a postulate?

a statement that can be proven

what is a theorem?

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

Defines the measure of an angle

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