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SSS (side, side, side)

ASA (angle, side, angle)

SAS (side, angle, side)

AAS (angle, angle, side)

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

If two angles and the included side of one triangle are congr…

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

If two angles and a side opposite one of the angles in one tr…

SSS (side, side, side)

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

ASA (angle, side, angle)

If two angles and the included side of one triangle are congr…

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle-Side (AAS) Congruence

If three sides of one triangle are congruent to three sides o…

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

If two angles and the included side of one triangle are congr…

If two angles and the non-included side of one triangle are c…

Side-Side-Side (SSS) Congruence

If three sides of one triangle are congruent to three sides o…

Side-Angle-Side (SAS) Congruence

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

SAS

ASA

AAS

SSS

Two triangles are congruent if two sides in the included angl…

Two triangles are congruent if two angles and the included si…

Two triangles are congruent if two angles and the consecutive…

If three sides of one triangle are congruent to three sides o…

SAS

Two triangles are congruent if two sides in the included angl…

ASA

Two triangles are congruent if two angles and the included si…

definition of congruence

definition of midpoint

definition of angle bisector

definition of perpendicular lines

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

the point that divides a segment into two congruent segments

the ray that divides an angle into two congruent angles

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…

definition of midpoint

the point that divides a segment into two congruent segments

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle- Side)

if three sides of one triangle are congruent to three sides o…

if two sides and the included angle of one triangle are congr…

if two angles and the included side of one triangle are congr…

if two angles and a nonincluded side of one triangle are cong…

SSS (Side-Side-Side)

if three sides of one triangle are congruent to three sides o…

SAS (Side-Angle-Side)

if two sides and the included angle of one triangle are congr…

Congruence

Midpoint

Angle Bisector

Perpendicular Lines

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

the point that divides a segment into two congruent segments

the ray that divides an angle into two congruent angles

lines that intersect to form right angles or 90°

Congruence

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

Midpoint

the point that divides a segment into two congruent segments

Midpoint

Segment bisector

Angle bisector

Perpendicular lines

A point that divides a segment into two congruent parts

A segment that divides a segment into two congruent parts

A segment that divides an angle into two congruent parts

Two lines that intersect to form right angles

Midpoint

A point that divides a segment into two congruent parts

Segment bisector

A segment that divides a segment into two congruent parts

side side side (SSS)

side angle side (SAS)

hypotenuse leg (HL)

angle angle side (AAS)

if three sides of one triangle are congruent to three sides o…

If two sides and the included angle are congruent to two side…

If the hypotenuse (the side across from the right angle) and…

If two angles and a non included side of one triangle are con…

side side side (SSS)

if three sides of one triangle are congruent to three sides o…

side angle side (SAS)

If two sides and the included angle are congruent to two side…

CPCTC

CSSPT

AA~

SAS~

Corresponding parts of congruent triangles ar congruent

Corresponding sides of similar triangles are proprtional

Angle angle similar

Side angle side similar

CPCTC

Corresponding parts of congruent triangles ar congruent

CSSPT

Corresponding sides of similar triangles are proprtional

SAS

SSS

ASA

AAS

requires two sides and an angle. The angle must be between th…

requires three sides

requires two angles and a side. The side must be between the…

requires two angles and a side. The side is not between the t…

SAS

requires two sides and an angle. The angle must be between th…

SSS

requires three sides

Segment Bisector

Angle Bisector

Intersecting Lines

Vertical Angles

Segment Bisector > midpoint... Midpoint > 2 = segments

Angle Bisector > 2 = angles

Intersecting Lines > Vertical Angles... Vertical Angles > 2 = A…

Vertical Angles > 2 = Angles

Segment Bisector

Segment Bisector > midpoint... Midpoint > 2 = segments

Angle Bisector

Angle Bisector > 2 = angles

Altitude of a triangle

Angle bisector of a triangle

Median of a triangle

Right angles

A line segment drawn from any vertex of a triangle ,perpendic…

A line segment that bisects any angle of the triangle and ter…

A line segment that joins any vertex of the triangle to the m…

all right angles are congruent

Altitude of a triangle

A line segment drawn from any vertex of a triangle ,perpendic…

Angle bisector of a triangle

A line segment that bisects any angle of the triangle and ter…

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

prove three (3) sets of corresponding sides congruent to each…

prove two (2) sets of corresponding sides congruent to each o…

prove two (2) sets of corresponding angles congruent to each…

prove two sets of corresponding angles congruent to each othe…

Side-Side-Side (SSS)

prove three (3) sets of corresponding sides congruent to each…

Side-Angle-Side (SAS)

prove two (2) sets of corresponding sides congruent to each o…

SAS

SSS

ASA

HL

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

If the three sides of one triangle is congruent to threats si…

If two angles and the included side of one triangle are congr…

If the hypotenuse and the leg of one triangle are congruent t…

SAS

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

SSS

If the three sides of one triangle is congruent to threats si…

Definition of Congruence

Definition of Midpoint

Definition of Angle Bisector

Definition of Perpendicular Lines

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

The point that divides a segment into two congruent segments

The ray that divides an angle into two congruent angles

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…

Definition of Midpoint

The point that divides a segment into two congruent segments

Side Side Side Congruence (SSS)

Side Angle Side Congruence (SAS)

Angle Side Angle Congruence (ASA)

Angle Angle Side Congruence (AAS)

If three sides of one triangle are congruent to three sides o…

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

If two angles and the included side of one triangle are congr…

If two angles and the non-included side of one triangle are c…

Side Side Side Congruence (SSS)

If three sides of one triangle are congruent to three sides o…

Side Angle Side Congruence (SAS)

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

Right Angle Congruence Theorem

Linear pair theorem

Definition of perpindicular lines

Adjacent

If two angles are right angles, then they are congruent. (Mus…

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

Perpindicular lines form right angles.

If two lines are perpinducular, then they form congruent adja…

Right Angle Congruence Theorem

If two angles are right angles, then they are congruent. (Mus…

Linear pair theorem

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

Definition of congruence

Midpoint

Angle bisector

Perpendicular lines

Having the exact same shape and size which allows the exact s…

A point that divides an angle into two congruent segments

A line that divides an angle into two congruent angle measure…

Lines that intersect to form 90° angles

Definition of congruence

Having the exact same shape and size which allows the exact s…

Midpoint

A point that divides an angle into two congruent segments

CPCTC

SSS

SAS

ASA

Corresponding Parts of Congruent Triangles are Congruent

Side Side Side - have to prove all 3 sides are congruent

Side Angle Side - 2 congruent sides with angles they create c…

Angle Side Angle - 2 congruent angles with the sides between…

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

SSS

Side Side Side - have to prove all 3 sides are congruent

SAS is congruent to SAS

AAS is congruent to AAS

HL is congruent to HL

SSS is congruent to SSS

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

if two angles and a non-included side of one triangle are con…

If the hypotenuse and a leg of one right triangle are congrue…

Two triangles are congruent if all 3 sets of corresponding si…

SAS is congruent to SAS

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

AAS is congruent to AAS

if two angles and a non-included side of one triangle are con…

Adjacent angles

Linear pairs

Supplementary angles

Complementary angles

Angles that share a common ray

2 adjacent angles that form a line=180

2 angles that add up to 180

2 angles that add up to 90

Adjacent angles

Angles that share a common ray

Linear pairs

2 adjacent angles that form a line=180

Definition of Congruent Polygons

CPCTC

Third Angles Theorem

Exterior Angle Theorem

Two polygons are congruent if and only if their corresponding…

Congruent Parts of Congruent Triangles are Congruent

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

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

Definition of Congruent Polygons

Two polygons are congruent if and only if their corresponding…

CPCTC

Congruent Parts of Congruent Triangles are Congruent

SSS Postulate

SAS Postluate

ASA Postulate

AAS Theorem

if 3 sides of 1 triangle is congruent to another 3 sides of a…

if 2 sides and the includes angle of 1 triangle are congruent…

if 2 angles and one included side of 1 triangle are congruent…

If 2 angles and a non-included side of one triangle are congr…

SSS Postulate

if 3 sides of 1 triangle is congruent to another 3 sides of a…

SAS Postluate

if 2 sides and the includes angle of 1 triangle are congruent…

SAS

AAS

HL

SSS

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

if two angles and a non-included side of one triangle are con…

If the hypotenuse and a leg of one right triangle are congrue…

Two triangles are congruent if all 3 sets of corresponding si…

SAS

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

AAS

if two angles and a non-included side of one triangle are con…

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (…

2 pairs of congruent angles and one pair of congruent sides (…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

What does CPCTC stand for?

Tells you to draw a box and prove 2 <'…

Extend lines. Proves 2 <'s AI.

Tells you to label two sides equal (co…

Corresponding Parts of Congruent Triangles are Congruent.

Perpendicular

Parallel

Midpoint

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent.

Tells you to draw a box and prove 2 <'…

Perpendicular

The Properties of Operations

Associative property of addition

Commutative prop. of addition

Additive identity property of 0

...

(a+b)+c=a+(b+c) ... (3+5)+7=3+(5+7)

a+b=b+a... (4x-5)+9=9+(4x-5)

a+0=0+a=a... -12+0=-12 0-12=-12

The Properties of Operations

...

Associative property of addition

(a+b)+c=a+(b+c) ... (3+5)+7=3+(5+7)

Riflexive Property

Subtraction Property

Equilateral

Isosceles

when a side length takes equal part in both triangles, and th…

m1 + m2 + m3 = m3 + m4 ... -m3 -m3... m1 + m2 = m4... (shows congru…

Triangle with all three congruent sides

Triangle with atleast two congruent sides

Riflexive Property

when a side length takes equal part in both triangles, and th…

Subtraction Property

m1 + m2 + m3 = m3 + m4 ... -m3 -m3... m1 + m2 = m4... (shows congru…

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (…

2 pairs of congruent angles and one pair of congruent sides (…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

Right angle

angle bisector

segment bisector

perpendicular

if 1 angle - a right angle is 90 degrees... if 2 or more angles…

angle 1 and angle 2 are congruent ... - angle bisector bisects a…

line AM is congruent to line MB... - segment bisector bisects a…

(+) angle 1,2,3,4 are right angles... - perpendicular lines inte…

Right angle

if 1 angle - a right angle is 90 degrees... if 2 or more angles…

angle bisector

angle 1 and angle 2 are congruent ... - angle bisector bisects a…

angle

Adjacent Angles

Alternate Exterior Angles

Alternate Interior Angles

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

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

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

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

angle

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

Adjacent Angles

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

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (…

2 pairs of congruent angles and one pair of congruent sides (…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

SSS Postulate

SAS Postluate

ASA Postulate

AAS Theorem

if 3 sides of 1 triangle are congruent to 3 sides of a 2nd tr…

if 2 sides and the included angle of 1 triangle are congruent…

if 2 angles and the included side of 1 triangle are congruent…

If 2 angles and a non-included side of one triangle are congr…

SSS Postulate

if 3 sides of 1 triangle are congruent to 3 sides of a 2nd tr…

SAS Postluate

if 2 sides and the included angle of 1 triangle are congruent…

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (…

2 pairs of congruent angles and one pair of congruent sides (…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

SSS

SAS

ASA

AAS

If 3 sides of the triangle are congruent to 3 sides of a seco…

If 2 sides and the included angle of one triangle are congrue…

If two angles and the included side of one triangle are congr…

If two angles and a non included side of one triangle are con…

SSS

If 3 sides of the triangle are congruent to 3 sides of a seco…

SAS

If 2 sides and the included angle of one triangle are congrue…

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (…

2 pairs of congruent angles and one pair of congruent sides (…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

Midpoint

Congruent Angles

Perpendicular Lines

Vertical Angles

point that divides the segment into two congruent segments

angles that have = measurements

2 lines that intersect to form right ∠'s

Two congruent non adjacent angles of intersecting lines

Midpoint

point that divides the segment into two congruent segments

Congruent Angles

angles that have = measurements

SSS Postulate

SAS Postulate

ASA Postulate

AAS Theorem

if 3 sides of 1 triangle is congruent to another 3 sides of a…

if 2 sides and the includes angle of 1 triangle are congruent…

if 2 angles and one included side of 1 triangle are congruent…

If 2 angles and a non-included side of one triangle are congr…

SSS Postulate

if 3 sides of 1 triangle is congruent to another 3 sides of a…

SAS Postulate

if 2 sides and the includes angle of 1 triangle are congruent…

Triangle Angle-Sum Theorem

Exterior Angles

Remote Interior Angles

Scalene Triangle

The sum of all angles of a triangle is 180 degrees.

Angle formed by extending one side. Equal to the sum of its r…

Angles non-adjacent to exterior angle.

A triangle with no congruent sides.

Triangle Angle-Sum Theorem

The sum of all angles of a triangle is 180 degrees.

Exterior Angles

Angle formed by extending one side. Equal to the sum of its r…

SAS Triangle Congruence

AAS Triangle Congruence

ASA Triangle Congruence

SSS Triangle Congruence

two pairs of corresponding sides congruent and the AND the an…

two pairs of corresponding angles congruent and one pair of c…

two pairs of corresponding angles congruent AND the sides bet…

three pairs of corresponding sides congruent

SAS Triangle Congruence

two pairs of corresponding sides congruent and the AND the an…

AAS Triangle Congruence

two pairs of corresponding angles congruent and one pair of c…

Intersecting Lines Create

Parallel Lines Create

When triangles share an angle you use

Similarity Proving Methods

Vertical Angles

Alternate Interior Angles or... Corresponding Angles

The Reflexive Property

AA, SAS and SSS Similarity

Intersecting Lines Create

Vertical Angles

Parallel Lines Create

Alternate Interior Angles or... Corresponding Angles

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

perpendicular lines form right angles

how to tell that two angles are supp (2)

how to tell that two angles are comp

how to tell that perp angles are equal…

perp lines def

1. the exterior sides of 2 adj angles are opposite rays -> su…

the exterior sides of 2 adj angles are perp -> comp

1. they are right angles -> all right angles are =... 2. two adj…

perpendicular lines form right angles

perp lines def

how to tell that two angles are supp (2)

1. the exterior sides of 2 adj angles are opposite rays -> su…