# Study sets matching "kapitel 2 math geometry proofs"

Study sets

Diagrams

Classes

Users

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Corresponding angles Postulate

Alternate Interior Angles Theorem

Alternate Exterior Angles Theorem

Consecutive Interior Angles Theorem

If lines m and n are parallel, Then corresponding angles forme…

CONVERSE OF ALTERNATE INTERIOR ANGLES... If the alternate interio…

If lines are parallel, Then the alternate exterior angles form…

If lines are parallel, Then consecutive interior angles formed…

Corresponding angles Postulate

If lines m and n are parallel, Then corresponding angles forme…

Alternate Interior Angles Theorem

CONVERSE OF ALTERNATE INTERIOR ANGLES... If the alternate interio…

SSS

SAS

Angle addition postulate

Segment Addition Postulate

postulate stating that when two triangles have corresponding s…

Triangles are congruent if any pair of corresponding sides and…

If point B lies in the interior of angle AOC, then. . The post…

SAP, if B is between segment AC, then AB+BC=AC

SSS

postulate stating that when two triangles have corresponding s…

SAS

Triangles are congruent if any pair of corresponding sides and…

Given, to prove, figure, statements, re…

Given, figure, previous statements

Congruent

Congruent segments

5 parts to a deductive proof

Three sources of statements

Two objects that have the same size and shape

Segments that have equal lengths

Given, to prove, figure, statements, re…

5 parts to a deductive proof

Given, figure, previous statements

Three sources of statements

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 ac=bc

if a=b and c doesnt equal 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

triangle sum theorem

exterior angle theorem

definition of congruent triangles

Third angles theorem

the some of interior angles in a triangle is 180 degrees

an exterior angle is equal to the sum of the two remote interi…

two polygons are congruent if and only if all pairs of corresp…

if two angles on one triangle are congruent to the two angles…

triangle sum theorem

the some of interior angles in a triangle is 180 degrees

exterior angle theorem

an exterior angle is equal to the sum of the two remote interi…

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Complementary Angles

Vertical angles

Substitution/ transitive

Perpendicular

Two angles that the sum equals 90°

each of the pairs of opposite angles made by two intersecting…

If a is congruent to B and B is congruent to c, then a is cong…

Two lines that intersect and form a right angle.

Complementary Angles

Two angles that the sum equals 90°

Vertical angles

each of the pairs of opposite angles made by two intersecting…

Segment Addition Postulate

Definition of a Congruent Segment

Definition of a Segment Bisector

Definition of a Midpoint

If three points A, B, C are collinear and B is between A and C…

Segments that have the same length (Used when you switch from…

a line, segment, ray, or plane that intersects a segment at it…

divides the segment into two congruent segments

Segment Addition Postulate

If three points A, B, C are collinear and B is between A and C…

Definition of a Congruent Segment

Segments that have the same length (Used when you switch from…

inductive reasoning

conjecture

counterexample

statement

A type of logic in which generalizations are based on a large…

A guess based on incomplete evidence

an example that proves a statement false

A sentence that is either true or false.

inductive reasoning

A type of logic in which generalizations are based on a large…

conjecture

A guess based on incomplete evidence

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 ac=bc

if a=b and c does not = 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

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Deductive Reasoning

Inductive Reasoning

Example Inductive Reasoning

Conjecture

Apply definitions, general statements, and already proven theo…

A way of drawing a general conclusion from special cases by ex…

All numbers in the set are multiplied by 3... The sum of the digi…

A conclusion developed by generalizing an idea using the induc…

Deductive Reasoning

Apply definitions, general statements, and already proven theo…

Inductive Reasoning

A way of drawing a general conclusion from special cases by ex…

Midpoint Theorem

Segment Addition Postulate

Reflexive Property

Symmetric Property

if m is the midpoint of AB, then AM is congruent to MB

if b is between A and C, then AB+BC=AC

AB is congruent to AB; angle ABC is congruent to ABC (can be u…

if AB is congruent to CD, then CD is congruent to AB

Midpoint Theorem

if m is the midpoint of AB, then AM is congruent to MB

Segment Addition Postulate

if b is between A and C, then AB+BC=AC

angle

Adjacent Angles

Alternate Exterior Angles

Alternate Interior Angles

Angles are created by two distinct rays that share a common en…

Angles in the same plane that have a common vertex and a... commo…

Alternate exterior angles are pairs of angles formed... when a th…

Alternate interior angles are pairs of angles formed... when a th…

angle

Angles are created by two distinct rays that share a common en…

Adjacent Angles

Angles in the same plane that have a common vertex and a... commo…

Segment Addition

Angle Addition Postulate

Def. of Midpoint

Def. of Angle Bisector

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

If B is on the interior of ∡AOC, then m∡AOB + m∡BOC= m∡AOC

M is the midpoint of segment AB IFF segment AM ≅ segment MB

ray BX is the angle bisector of ∡ABC IFF m∡ABX = m∡XBC (or ∡AB…

Segment Addition

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

Angle Addition Postulate

If B is on the interior of ∡AOC, then m∡AOB + m∡BOC= m∡AOC

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + 3 = b + 3

Reflexive Property of Equality

a = a

Symmetric Property of Equality

If a = b... Then b = a

Segment Addition

Angle Addition Postulate

Def. of Midpoint

Def. of Angle Bisector

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

If B is on the interior of ∡AOC, then m∡AOB + m∡BOC= m∡AOC

M is the midpoint of segment AB IFF segment AM ≅ segment MB

ray BX is the angle bisector of ∡ABC IFF m∡ABX = m∡XBC (or ∡AB…

Segment Addition

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

Angle Addition Postulate

If B is on the interior of ∡AOC, then m∡AOB + m∡BOC= m∡AOC

circumcenter

perpendicular bisector

bisect

centroid

where all the perpendicular bisectors of a triangle intersect

Bisects a segment and is perpendicular to it.

to cut exactly in half

The point of concurrency of the medians of a triangle

circumcenter

where all the perpendicular bisectors of a triangle intersect

perpendicular bisector

Bisects a segment and is perpendicular to it.

Definition of Congruence

Definition of a Midpoint

Definition of Angle Bisector

Definition of Perpendicular Lines

Having the exact same size and shape and there by having the e…

The point that divides a segment into two congruent halves.

The ray that divides an angle into two congruent halves.

Lines that intersect to form right angles or 90 degrees.

Definition of Congruence

Having the exact same size and shape and there by having the e…

Definition of a Midpoint

The point that divides a segment into two congruent halves.

Isosceles triangle

equilateral triangle

right triangle

rhombus

show that 2 sides are =. Use distance formula

show that 3 sides are =. Use distance formula

show that there is 1 right angle. Use slope formula

show that 4 sides are =. Use distance formula

Isosceles triangle

show that 2 sides are =. Use distance formula

equilateral triangle

show that 3 sides are =. Use distance formula

Parallelogram Properties

Rectangle Properties

Rhombus Properties

Square Properties

1. Opposite sides are congruent... 2. Opposite angles are congrue…

1. All properties of a parallelogram... 2. Diagonals are congruent

1. All properties of a parallelogram... 2. Diagonals are perpendi…

1. All properties of a parallelogram... 2. All properties of a re…

Parallelogram Properties

1. Opposite sides are congruent... 2. Opposite angles are congrue…

Rectangle Properties

1. All properties of a parallelogram... 2. Diagonals are congruent