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scalene

isosceles

47º

78º

Find the measures of the sides of ∆ABC and classify the trian…

Find the measures of the sides of KPL and classify the triang…

m∠1=?

m∠2=?

scalene

Find the measures of the sides of ∆ABC and classify the trian…

isosceles

Find the measures of the sides of KPL and classify the triang…

Definition of Congruent Triangles

C.P.C.T.C

SSS Postulate

SAS Postulate

2 triangles are congruent if and only if their corresponding…

Corresponding parts of congruent triangles are congruent. ( D…

If 3 sides of one triangle are congruent to 3 sides of anothe…

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

Definition of Congruent Triangles

2 triangles are congruent if and only if their corresponding…

C.P.C.T.C

Corresponding parts of congruent triangles are congruent. ( D…

Triangle Sum Theorem

Exterior Angle Theorem

Flow Proof

Corollary

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

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

A flow proof uses statements in boxes, with reasons beneath t…

A statement that follows directly from a theorem.

Triangle Sum Theorem

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

Exterior Angle Theorem

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

Congruent Polygons

If two angles of one triangle are cong…

Side-Side-Side Postulate

Side-Angle-Side Postulate

have congruent corresponding parts

the third angles are congruent

If 3 sides of 1 triangle are congruent to the 3 sides of anot…

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

Congruent Polygons

have congruent corresponding parts

If two angles of one triangle are cong…

the third angles are congruent

triangle

scalene triangle

isosceles triangle

equilateral triangle

a polygon with three sides

a triangle with no congruent sides

a triangle with at least 2 congruent sides

a triangle with all congruent sides

triangle

a polygon with three sides

scalene triangle

a triangle with no congruent sides

Congruent polygons

3rd angle theorem

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

Polygon with congruent corresponding sides and congruent corr…

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

If 3 sides of a triangle are congruent to 3 sides of another…

If 2 sides and an **included angle** of one triangle are congru…

Congruent polygons

Polygon with congruent corresponding sides and congruent corr…

3rd angle theorem

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

Acute

Obtuse

Equilateral

Equiangular

A triangle that has 3 angles less than 90 degrees

A triangle that has 1 angle more than 90 degrees

A triangle that has 3 sides congruent

A triangle that has 3 angles congruent

Acute

A triangle that has 3 angles less than 90 degrees

Obtuse

A triangle that has 1 angle more than 90 degrees

scalene triangle

isosceles triangle

equilateral triangle

equiangular triangle

A triangle with 3 uneven sides

A triangle with two sides of equal length

A triangle with three equal sides

a triangle with all three angles equal

scalene triangle

A triangle with 3 uneven sides

isosceles triangle

A triangle with two sides of equal length

Triangle Sum Theorem (4.1)

Exterior Angle Theorem (4.1)

Corollary to the Triangle Sum Theorem…

Definition of Congruent Figures (4.2)

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

The measure of an exterior angle of a triangle is non-adjacen…

The acute angles of a right triangle are complementary.

All the parts of one figure are congruent to the correspondin…

Triangle Sum Theorem (4.1)

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

Exterior Angle Theorem (4.1)

The measure of an exterior angle of a triangle is non-adjacen…

Congruent Triangles

SSS Postulate

ASA Postulate

SAS Postulate

Two triangles are congruent if and only if there is a corresp…

If each of the three sides of one triangle are congruent resp…

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

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

Congruent Triangles

Two triangles are congruent if and only if there is a corresp…

SSS Postulate

If each of the three sides of one triangle are congruent resp…

Acute Triangle

Equiangular Triangle

Obtuse Triangle

Right Triangle

3 acute angles/all angles less than 90°

3 congruent angles/all angles are 60

One obtuse angle/has an angle greater than 90

One right angle

Acute Triangle

3 acute angles/all angles less than 90°

Equiangular Triangle

3 congruent angles/all angles are 60

congruent

SSS Postulate

SAS Postulate

ASA Postulate

-if two figures have the same shape and size... -two triangles a…

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…

congruent

-if two figures have the same shape and size... -two triangles a…

SSS Postulate

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

Dilation

Translation

Reflection across y axis

Reflection across x-axis

With scale factor k>0 and the center (0,0) males (x,y) to (Kx…

(X,y) then (x+a,y+b)

(X,y) then (-x,y)

(X,Y) then (x,-y)

Dilation

With scale factor k>0 and the center (0,0) males (x,y) to (Kx…

Translation

(X,y) then (x+a,y+b)

equiangular triangle

equilateral triangle

isosceles triangle

scalene triangle

a triangle with all congruent angles

a triangle with all congruent sides

a triangle with at least two sides congruent

triangle with no sides congruent

equiangular triangle

a triangle with all congruent angles

equilateral triangle

a triangle with all congruent sides

Adjacent angles

Complementary angles

Supplementary angles

Linear pair of angles

Two angles in the same plane that have a common vertex and a…

Two angles, the sum of whose degree measure is 90

Two angles, the sum of whose degree measure is 180

2 adjacent angles whose sum is a straight angle

Adjacent angles

Two angles in the same plane that have a common vertex and a…

Complementary angles

Two angles, the sum of whose degree measure is 90

Congruent figures

Definition of congruent triangles

C.P.C.T.C

SSS postulate

Figures hat have the same size and shape

2 triangles are congruent IF AND ONLY IF their corresponding…

Corresponding parts of congruent triangles are congruent (int…

(Side-side-side postulate) if 3 sides of a triangle are congr…

Congruent figures

Figures hat have the same size and shape

Definition of congruent triangles

2 triangles are congruent IF AND ONLY IF their corresponding…

congruent figures

definition of congruent triangles

CPCTC

SSS postulate

same size and shape

2 triangles are congruent **iff** their corresponding parts are…

corresponding parts of congruent triangles are congruent

If 3 sides of 1 triangle are congruent to 3 sides of another…

congruent figures

same size and shape

definition of congruent triangles

2 triangles are congruent **iff** their corresponding parts are…

Congruent figures

Definition of congruent triangles

CPCTC

Side-side-side postulate

Same size and shape

2 triangles are congruent iff their corresponding parts are c…

Corresponding parts of congruent triangles are congruent.

If 3 sides of 1 triangle are congruent to 3 sides of another…

Congruent figures

Same size and shape

Definition of congruent triangles

2 triangles are congruent iff their corresponding parts are c…

Translation

Reflection

Dilation

acute triangle

(x,y) → (x + a, y + b) Translation a units horizontally and b…

Reflection across y-axis : (x,y) → (-x,y)... Reflection across x…

(x,y) → (kx,ky) , k > 0 Dilation with a scale factor k and ce…

three acute angles

Translation

(x,y) → (x + a, y + b) Translation a units horizontally and b…

Reflection

Reflection across y-axis : (x,y) → (-x,y)... Reflection across x…

Congruent polygons

Corollary

Legs of an isosceles triangle

Base of an isosceles triangle

_______have congruent corresponding parts--their matching sid…

A theorem that can easily be proved using another theorem.

Congruent sides of an isosceles triangle.

Side not congruent in a isosceles triangle (3rd/remaining sid…

Congruent polygons

_______have congruent corresponding parts--their matching sid…

Corollary

A theorem that can easily be proved using another theorem.

Third Angle Theorem (TAT)

Side-side-side Postulate (SSS)

included angle

Side-angle-side Postulate (SAS)

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

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

an angle between two sides of a triangle

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

Third Angle Theorem (TAT)

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

Side-side-side Postulate (SSS)

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

triangle

interior angles

exterior angles

corollary to a theorem

a polygon with three sides

when the sides of a triangle are extended, the three original…

when the sides of a triangle are extended, the angles that ar…

a statement that can be proved easily using the theorem

triangle

a polygon with three sides

interior angles

when the sides of a triangle are extended, the three original…

detour proof

Mid-point formula

Theorem (4.1)

Theorem (4.3)

a proof in which it is necessary to prove more than one pair…

used to find the coordinates of the midpoint of a segment in…

M= (Xm, Ym) = [(x₁+ x₂)/2 , (y₁+ y₂)/2]

If two angles are both supplementary and congruent, then they…

detour proof

a proof in which it is necessary to prove more than one pair…

Mid-point formula

used to find the coordinates of the midpoint of a segment in…

Triangle sum theorem

Third angles theorem

Converse of isosceles triangles

Isosceles triangle conjecture

The measures of 3 angles in 2 triangles add up to 180°

If two angles in a triangle are congruent to two angles in an…

If two angles of a triangle are congruent then it is an isosc…

If a triangle is isosceles then the base angles are congruent

Triangle sum theorem

The measures of 3 angles in 2 triangles add up to 180°

Third angles theorem

If two angles in a triangle are congruent to two angles in an…

triangle

scalene triangle

isosceles triangle

equilateral triangle

a polygon with three sides

a triangle with no congruent sides

a triangle with at least 2 congruent sides

a triangle with all congruent sides

triangle

a polygon with three sides

scalene triangle

a triangle with no congruent sides

Interior Angles

Exterior Angles

Corollary to a Theorem

Congruent Figures

The triangles original angles

The angles that form linear regression interior angles

A statement that can be proved easily using the theorem

All parts of one figure are congruent to the corresponding pa…

Interior Angles

The triangles original angles

Exterior Angles

The angles that form linear regression interior angles

acute triangle

equiangular triangle

obtuse triangle

right triangle

a triangle with all angles measuring less than 90˚

a triangle with all angles congruent

a triangle with one angle measuring over 90˚

a triangle with one angle measuring exactly 90˚ (right angle)

acute triangle

a triangle with all angles measuring less than 90˚

equiangular triangle

a triangle with all angles congruent

congruent

common side

SSS Postulate

SAS Postulate

whenever two figures have the same side and shape

the side used by two polygons

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

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

congruent

whenever two figures have the same side and shape

common side

the side used by two polygons

Triangle Third Angle Theorem

SSS

SAS

ASA

If 2 angles of a triangle are congruent to 2 angles of anothe…

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

If two sides and the included angle (angle in between those t…

If 2 angles and the included side of one triangle are congrue…

Triangle Third Angle Theorem

If 2 angles of a triangle are congruent to 2 angles of anothe…

SSS

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

Parallelogram

Theorem 4.1.1

Corollary 4.1.2

Corollary 4.1.3

A quadrilateral in both pairs of opposites are parallel.

A diagonal of a parallelogram separates it into two congruent…

The opposite angles of a parallelogram are congruent.

The opposite sides of a parallelogram are congruent.

Parallelogram

A quadrilateral in both pairs of opposites are parallel.

Theorem 4.1.1

A diagonal of a parallelogram separates it into two congruent…

Equidistance Theorem

Converse of Equidistance Theorem

// Lines Slope

// Lines Slope Converse

If 2 points are equidistance to the endpoints of a segment th…

Any point on the perpendicular bisector of a segment is equid…

If two nonvertical lines are parallel, then their slopes are…

If the slopes of two nonvetical lines are equal, then their l…

Equidistance Theorem

If 2 points are equidistance to the endpoints of a segment th…

Converse of Equidistance Theorem

Any point on the perpendicular bisector of a segment is equid…

CPCTC

Legs (isosceles triangle)

Base

Vertex Angles

Corresponding Parts of Congruent Triangles are Congruent

The congruent sides of an isosceles triangle

The third side of an isosceles triangle

Angle formed by the legs of an isosceles triangle

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

Legs (isosceles triangle)

The congruent sides of an isosceles triangle

4 Angle Measures and descriptions

3 Side Lengths and descriptions

Triangle Sum Thm

Exterior Angle Thm

1. Acute Angle- three acute angles ... 2. Equiangular Angle- thr…

1. Equilateral- three congruent sides... 2. Isosceles- AT LEAST…

the sum of the angle measures of a triangle is 180 degrees

the measure of of an exterior angle of a triangle is equal to…

4 Angle Measures and descriptions

1. Acute Angle- three acute angles ... 2. Equiangular Angle- thr…

3 Side Lengths and descriptions

1. Equilateral- three congruent sides... 2. Isosceles- AT LEAST…

triangle

interior angles

exterior angles

corollary to a theorem

a polygon with three sides

when the sides of a polygon are extended, these are the origi…

angles that form linear pairs with the interior angles

a statement that can be proved easily using the theorem

triangle

a polygon with three sides

interior angles

when the sides of a polygon are extended, these are the origi…

Definition of Congruence

CPCTC

Isosceles Triangle Theorem

Isosceles Triangle Theorem Converse

When 2 figures have the same size and shape

Two triangles are congruent if and only if their vertices can…

If two sides of a triangle are congruent, then the angles opp…

If two angles of a triangle are congruent, then the sides opp…

Definition of Congruence

When 2 figures have the same size and shape

CPCTC

Two triangles are congruent if and only if their vertices can…

Median

Midsegment

Altitude

Centroid

Line legment from the vertex to the midpoint... Of the opposite…

Segment whose end points are the midpoints of two sides of a…

Line segment from vertex perpendicular to the opposite side

Point of concurrency of the medians

Median

Line legment from the vertex to the midpoint... Of the opposite…

Midsegment

Segment whose end points are the midpoints of two sides of a…

acute triangle

acute

equiangular triangle

congruent

a triangle in which all of the angles are acute angles

an angle less than 90 degrees

a triangle with all angles congruent

having the same size and shape

acute triangle

a triangle in which all of the angles are acute angles

acute

an angle less than 90 degrees

Scalene Triangle

Isosceles Triangle

Equilateral Triangle

Equiangular Triangle

A triangle with no two sides congruent

A triangle with at least two sides congruent

A triangle with all three sides congruent

A triangle with all three angles congruent

Scalene Triangle

A triangle with no two sides congruent

Isosceles Triangle

A triangle with at least two sides congruent

base angles of an isosceles triangle

base of an isosceles triangle

congruent polygons

corollary

an isosceles triangle is a triangle that has at least two con…

an isosceles that is a triangle with at least two congruent s…

polygons that have corresponding sides that are congruent and…

a theorem that can be proved easily using another theorem

base angles of an isosceles triangle

an isosceles triangle is a triangle that has at least two con…

base of an isosceles triangle

an isosceles that is a triangle with at least two congruent s…

Polygon

Congruent Polygons

Congruent Triangles

Scalene Triangle

a connected set of at least 3 line segments in the same plane…

2 polygons are congruent iff there is a correspondence betwee…

2 triangles are congruent iff there is a correspondence betwe…

iff it has no equal sides

Polygon

a connected set of at least 3 line segments in the same plane…

Congruent Polygons

2 polygons are congruent iff there is a correspondence betwee…

Triangle

Opposite sides

Opposite angles

Acute triangles

3 sided figure made up of segs called sides that intersect on…

angles are considered...

sides are considered...

3 acute angles

Triangle

3 sided figure made up of segs called sides that intersect on…

Opposite sides

angles are considered...