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SSS

SAS

Angle addition postulate

Segment Addition Postulate

postulate stating that when two triangles have corresponding…

Triangles are congruent if any pair of corresponding sides an…

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

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

SSS

postulate stating that when two triangles have corresponding…

SAS

Triangles are congruent if any pair of corresponding sides an…

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

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

Right Angle Congruence Theorem(RACT)

Vertical Angle Congruence Theorem(VACT)

Linear Pair Postulate(LPP)

Congruent (Comp.,Supp.) theorem

right angles are congruent

vertical angles are congruent

if 2 angles are a linear pair then they are supplementary

If two angles are (Comp.,Supp.) of the same angle then they a…

Right Angle Congruence Theorem(RACT)

right angles are congruent

Vertical Angle Congruence Theorem(VACT)

vertical angles are congruent

A state meant that can be written in a…

Part "p" of the statement comes after If

Part "q" of the statement comes after…

Using pattern and observations to dete…

Conditional Statement

Hypothesis

Conclusion

Inductive Reasoning

A state meant that can be written in a…

Conditional Statement

Part "p" of the statement comes after If

Hypothesis

Congruent Segements

Congruent Angles

Adjacent angles

Linear Pair

2 segments with the exact same lengths

2 angles that have the exact same measurement

2 angles with a common vertex point and common side

Pair of adjacent angles whose no common sides are opposite rays

Congruent Segements

2 segments with the exact same lengths

Congruent Angles

2 angles that have the exact same measurement

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

Isosceles triangle

Equilateral triangle

Right triangle

What type of lines form a right angle?

SHOW: ... - 2 sides = ... FORMULA: ... - Distance

SHOW:... - 3 sides = ... FORMULA: ... - Distance

SHOW: ... - 1 right angle... FORMULA: ... - Slope

Perpendicular Lines

Isosceles triangle

SHOW: ... - 2 sides = ... FORMULA: ... - Distance

Equilateral triangle

SHOW:... - 3 sides = ... FORMULA: ... - Distance

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

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…

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

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

divides the segment into two congruent segments

Segment Addition Postulate

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

Definition of a Congruent Segment

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

Side-Side-Side Similarity (SSS ~)

Side-Angle-Side Similarity (SAS ~)

Angle-Angle Similarity (AA ~)

Corresponding Angles In Parallel Lines

Where 3 sides of one triangle are proportional to 3 correspon…

Where 2 sides of one triangle are proportional to 2 correspon…

Where 2 angles of one triangle are congruent to 2 angles of a…

Are Congruent

Side-Side-Side Similarity (SSS ~)

Where 3 sides of one triangle are proportional to 3 correspon…

Side-Angle-Side Similarity (SAS ~)

Where 2 sides of one triangle are proportional to 2 correspon…

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

Given, to prove, figure, statements, r…

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, r…

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 is not equal to 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

Isosceles Triangle

Equilateral Triangles

Right Triangle

Rhombus

2 sides are equal, Distance Formula

3 sides are equal, Distance Formula

1 right angle, slope

4 sides are equal, Distance Formula

Isosceles Triangle

2 sides are equal, Distance Formula

Equilateral Triangles

3 sides are equal, Distance Formula

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

Supplementary Angles

Theorem

Vertical Angles

Two angles whose measures have a sum of 90 degrees

Two angles whose measures have a sum of 180 degrees

A statement that can be proven

Two angles formed by intercepting lines and facing in the opp…

Complementary Angles

Two angles whose measures have a sum of 90 degrees

Supplementary Angles

Two angles whose measures have a sum of 180 degrees

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 is not equal to 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

Inductive Reasoning

Conjecture

Counterexample

Conditional

is a type of reasoning that reaches conclusions based on a pa…

is a conclusion reached by using inductive reasoning.... ex: As…

an example showing that a statement is false.... ex:... STATEMENT:…

is an "if-then" statement.... ex: If you act politely, then you…

Inductive Reasoning

is a type of reasoning that reaches conclusions based on a pa…

Conjecture

is a conclusion reached by using inductive reasoning.... ex: As…

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

Law of Detachment

Law of Syllogism

Two Point Postulate

Line-Point Postulate

If the hypothesis of a true conditional statement is true, th…

Take two conditional statements and form a conclusion by comb…

Through any two points, there exists exactly one line.

A line contains at least two points.

Law of Detachment

If the hypothesis of a true conditional statement is true, th…

Law of Syllogism

Take two conditional statements and form a conclusion by comb…

Complementary

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 con…

Two lines that intersect and form a right angle.

Complementary

Two angles that the sum equals 90°

Vertical angles

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

Angle addition postulate

Segment addition postulate

Linear Pair Postulate

Vertical Angles Theorem

Measure of an angle equals sum of pairs

Measure of a segment equals sum of its parts

If two angles form a linear pair then they are supplementary

Vertical angles are congruent

Angle addition postulate

Measure of an angle equals sum of pairs

Segment addition postulate

Measure of a segment equals sum of its parts

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

Perpendicular Bisector Theorem

Converse of the Perpendicular Bisector…

Angle Bisector Theorem

Converse of the Angle Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

In a plane, if a point is equidistant from the endpoints of a…

If a point lies on the bisector of an angle, then it is equid…

If a point is in the interior of an angle and is equidistant…

Perpendicular Bisector Theorem

In a plane, if a point lies on the perpendicular bisector of…

Converse of the Perpendicular Bisector…

In a plane, if a point is equidistant from the endpoints of a…

Definition of Congruence

Definition of Bisector

Definition of Midpoint

Definition of Supplementary angles

switch between saying the lengths are equal to being congruent

to break into 2 different parts

the middle value creates 2 equal segments

sum of 2 angles that equal 180

Definition of Congruence

switch between saying the lengths are equal to being congruent

Definition of Bisector

to break into 2 different parts

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

Polygon Interior Angles Theorem

Corollary to the Polygon Interior Angl…

Polygon Exterior Angles Theorem

Parallel Opposite Sides Theorem

The sum of the measures of the interior angles of a convex n-…

The sum of the measures of the interior angles of a quadrilat…

The sum of the measures of the exterior angles of a convex po…

If a quadrilateral is a parallelogram, then its opposite side…

Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a convex n-…

Corollary to the Polygon Interior Angl…

The sum of the measures of the interior angles of a quadrilat…

Arc Addition Postulate

Tangent Line to Circle Theorem

External Tangent Congruence Theorem

Congruent Circles Theorem

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

In a plane, a line is tangent to a circle if and only if the…

Tangent segments from a common external point are congruent.

Two circles are congruent circles if and only if they have th…

Arc Addition Postulate

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

Tangent Line to Circle Theorem

In a plane, a line is tangent to a circle if and only if the…

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Theorem

Alternate Interior Angles Theorem

If there is a line and a point not on the line, then there is…

If there is a line and a point not on the line, then there is…

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

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

Parallel Postulate

If there is a line and a point not on the line, then there is…

Perpendicular Postulate

If there is a line and a point not on the line, then there is…

Triangle Sum Theorem

Exterior Angle Theorem

Corollary to the Triangle Sum Theorem

Reflexive Property of Triangle Congrue…

The sum of the measures of the interior angles of a triangle…

The measure of an exterior angle of a triangle is equal to th…

The acute angles of a right triangle are complementary.

For any triangle ABC, triangle ABC is congruent to triangle A…

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle…

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to th…

Pythagorean Theorem

Converse of the Pythagorean Theorem

Pythagorean Inequalities Theorem

45°-45°-90° Triangle Theorem

In a right triangle, the square of the length of the hypotenu…

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

If c²<a²+b², then ΔABC is acute.... If c²>a²+b², then ΔABC is ob…

In a 45°-45°-90° triangle, the hypotenuse is √2 times as long…

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenu…

Converse of the Pythagorean Theorem

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

Perimeters of Similar Polygons

Areas of Similar Polygons

Angle-Angle (AA) Similarity Theorem

Side-Side-Side (SSS) Similarity Theorem

If two polygons are similar, then the ratio of their areas is…

If two polygons are similar, then the ratio of their areas is…

If two angles of one triangle are congruent to two angles of…

If the corresponding side lengths of two triangles are propor…

Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their areas is…

Areas of Similar Polygons

If two polygons are similar, then the ratio of their areas is…

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

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…

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

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

divides the segment into two congruent segments

Segment Addition Postulate

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

Definition of a Congruent Segment

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

Triangle Angle Sum Theorem

Perpendicular

CPCTC

SSS

The angles in a triangle add to 180

If 2 lines are perpendicular, then they form right angles.

If 2 triangles are congruent, then corresponding sides and/or…

If 3 sides of one triangle are congruent to 3 corresponding s…

Triangle Angle Sum Theorem

The angles in a triangle add to 180

Perpendicular

If 2 lines are perpendicular, then they form right angles.

Complementary

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 con…

Two lines that intersect and form a right angle.

Complementary

Two angles that the sum equals 90°

Vertical angles

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

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

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 is not equal to 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

addition property of equality

subtraction property of equality

multiplication property of equality

division property of equality

adding the same thing to both sides

subtracting the same thing to both sides

multiplying the same thing on both sides

dividing the same thing on both sides

addition property of equality

adding the same thing to both sides

subtraction property of equality

subtracting the same thing to both sides