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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

Interior angles

Exterior angles

Corollary to a theorem

Polygon with 3 sides

When the sides are extended the angles are in the inside

When the sides are extended the angles are on the outside

A statement that can be proved easily with the theorem

Triangle

Polygon with 3 sides

Interior angles

When the sides are extended the angles are in the inside

acute triangle

auxiliary line

base

base angle

a triangle whose interior angles are all acute

a line that is added to a figure in a proof

the side opposite the vertex angle

an angle that has the base as a side with another angle

acute triangle

a triangle whose interior angles are all acute

auxiliary line

a line that is added to a figure in a proof

alternate exterior angles

alternate interior angles

consecutive interior angles

corresponding angles

On opposite sides of the transversal, outside the parallel li…

On opposite sides of the transversal, inside the parallel lines

On the same side of the transversal

Have different vertices

alternate exterior angles

On opposite sides of the transversal, outside the parallel li…

alternate interior angles

On opposite sides of the transversal, inside the parallel lines

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

Acute Triangle

All 3 sides of the triangle are congruent.

At least 2 sides of the triangle are congruent.

0 sides of the triangle are congruent.

The triangle has 3 acute angles.

Equilateral Triangle

All 3 sides of the triangle are congruent.

Isosceles Triangle

At least 2 sides of the triangle are congruent.

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

Interior Angles

Exterior Angles

Corollary

A polygon with three sides.

Angles inside the triangle that form the vertices.

Angles that form linear pairs with the interior angles (outsi…

A statement that can be proved easily using a given theorem.

Triangle

A polygon with three sides.

Interior Angles

Angles inside the triangle that form the vertices.

Scalene Triangles

Equilateral Triangle

Isosceles Triangle

Linear Pair

A triangle that has three unequal sides

A triangle with three equal sides

A triangle of two sides of equal length

Lines that add up to 180

Scalene Triangles

A triangle that has three unequal sides

Equilateral Triangle

A triangle with three equal sides

Right Angle

Acute Angle

Obtuse Angle

Acute Triangle

An angle that measures 90 degrees.

An angle that measures between 0 and 90 degrees.

An angle that measures between 90 and 180 degrees.

A triangle with three acute angles.

Right Angle

An angle that measures 90 degrees.

Acute Angle

An angle that measures between 0 and 90 degrees.

Base Angles of an Isosceles Triangle

Base of an Isosceles Triangle

Congruent Polygons

Corollary

If two sides of a triangle are congruent (legs), then the ang…

The third side of the triangle that is not the legs (opposite…

Congruent corresponding parts- their matching sides and angles

a theorem that can be proved easily using another theorem; us…

Base Angles of an Isosceles Triangle

If two sides of a triangle are congruent (legs), then the ang…

Base of an Isosceles Triangle

The third side of the triangle that is not the legs (opposite…

Side-Side-Side Congruence Postulate (S…

Angle-Side-Angle Congruence Theorem (A…

Side-Angle-Side Congruence Postulate (…

Side-Side-Angle Conjecture (SSA)

If the sides of one triangle are congruent to the sides of an…

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

If two sides and their included angle in one triangle are con…

In an SSA combination, if the given side opposite the given a…

Side-Side-Side Congruence Postulate (S…

If the sides of one triangle are congruent to the sides of an…

Angle-Side-Angle Congruence Theorem (A…

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

congruent figures

congruent polygons

two congruent triangles

Theorem 4-1

have the have the same size and shape

have congruent corresponding parts, matching sides, angles, a…

congruent when they have three pairs of congruent correspondi…

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

congruent figures

have the have the same size and shape

congruent polygons

have congruent corresponding parts, matching sides, angles, a…

triangle

equilateral triangle

isosceles triangle

scalene triangle

A figure formed by three segments joining at three points not…

A triangle with three congruent sides

A triangle that has 2 equal sides.

a triangle with no congruent sides

triangle

A figure formed by three segments joining at three points not…

equilateral triangle

A triangle with three congruent sides

Yes by Side-Angle-Side

YES by Side-Side-Side

YES by Angle-Angle-Side

YES by Angle-Side-Angle

Can you prove triangles congruent? If so, by what theorem?

Can you prove triangles congruent? If so, by what theorem?

Can you prove triangles congruent? If so, by what theorem?

Can you prove triangles congruent? If so, by what theorem?

Yes by Side-Angle-Side

Can you prove triangles congruent? If so, by what theorem?

YES by Side-Side-Side

Can you prove triangles congruent? If so, by what theorem?

triangle

scalene triangle

equilateral triangle

isosceles triangle

a figure formed by three segments joining three noncollinear…

a triangle with no congruent sides

a triangle with three congruent sides

a triangle with two congruent sides

triangle

a figure formed by three segments joining three noncollinear…

scalene triangle

a triangle with no congruent sides

Triangles can by classified by:

Acute triangles

obtuse triangles

equiangular triangles

by their angles or by their sides. All triangles have at leas…

3 acute angles

1 obtuse angle

3 congruent acute triangles

Triangles can by classified by:

by their angles or by their sides. All triangles have at leas…

Acute triangles

3 acute angles

congruent

congruent

congruent

congruent

when using Side Side Side (SSS) congruent to SSS, are you pro…

when using Side Angle Side (SAS) congruent to SAS, are you pr…

when using Angle Side Angle (ASA) congruent to ASA, are you p…

when using Hypotenuse Leg (HL) congruent to HL , are you prov…

congruent

when using Side Side Side (SSS) congruent to SSS, are you pro…

congruent

when using Side Angle Side (SAS) congruent to SAS, are you pr…

def of reflection image

reflection postulate (image/preimage)

figure transformation theorem

reflection postulate (orientation)

for a point P not on line M, the ___ ___ of P over line M is…

each preimage has exactly 1 image and vice versa

if a figure is determined by certain points, then its transfo…

if a preimage has clockwise orientation, its image has counte…

def of reflection image

for a point P not on line M, the ___ ___ of P over line M is…

reflection postulate (image/preimage)

each preimage has exactly 1 image and vice versa

perpendicular bisector

Hypotenuse-Leg Theorem

Hypotenuse-Angle Theorem

Leg-Angle Theorem

a segment that is perpendicular to another segment and bisect…

E and F are congruent angles; right angles cannot be used

Lines CB and FE are congruent and angles E and F are congruen…

perpendicular bisector

a segment that is perpendicular to another segment and bisect…

Hypotenuse-Leg Theorem

Acute Triangle

Equiangular Triangle

Obtuse Triangle

Right Triangle

A triangle with all angles less than 90 degrees

A triangle with all angles measuring the same

A triangle with one side more than 90 degrees

A triangle with one angle measuring exactly 90 degrees

Acute Triangle

A triangle with all angles less than 90 degrees

Equiangular Triangle

A triangle with all angles measuring the same

Coordinate Proof

Flow Proof

Remote Interior Angle

Auxiliary Line

Proofs that use figures in a coordinate plane and algebra to…

A proof that organizes statements in logical order, starting…

The angles of a triangle that are not adjacent to a given ext…

An extra line or segment drawn in a figure to help complete a…

Coordinate Proof

Proofs that use figures in a coordinate plane and algebra to…

Flow Proof

A proof that organizes statements in logical order, starting…

congruent figures

when are figures congruent?

how do we name congruent figures/ cong…

third angles theorem

figures that have the same size and slope

when corresponding sides and angle are congruent

name the corresponding vertices in order

if 2 angles in one triangle are congruent to 2 angles of anot…

congruent figures

figures that have the same size and slope

when are figures congruent?

when corresponding sides and angle are congruent

auxillary line

exterior angle

remote interior angles

flow proof

an extra line or segment drawn in a figure to help complete a…

an angle formed by one side of a triangle and the extension o…

the angles of a triangle that are not adjacent to a given ext…

a proof that organizes statements in logical order, starting…

auxillary line

an extra line or segment drawn in a figure to help complete a…

exterior angle

an angle formed by one side of a triangle and the extension o…

Perpendicular Lines

Perpendicular Bisector

Parallel Lines

Alternate Interior Angles

two lines that intersect to forma right angle

a line that bisects a line segment and in perpendicular to th…

lines that lie in the same plane and do not intersect

Interior angles that are on opposite sides of a transversal

Perpendicular Lines

two lines that intersect to forma right angle

Perpendicular Bisector

a line that bisects a line segment and in perpendicular to th…

auxiliary line

paragraph proof

Triangle Sum Conjecture

leg

An extra line or line segment drawn in a figure to help in a…

A logical explanation presented in the form of a paragraph.

The sum of the measures of the angles in every triangle is 18…

(of an isosceles triangle) One of the congruent sides of an i…

auxiliary line

An extra line or line segment drawn in a figure to help in a…

paragraph proof

A logical explanation presented in the form of a paragraph.

acute

equiangular

obtuse

right

a triangle that has 3 acute angles

a triangle that has 3 congruent acute sides (is a special kin…

a triangle that has 1 obtuse angle

a triangle that has 1 right angle

acute

a triangle that has 3 acute angles

equiangular

a triangle that has 3 congruent acute sides (is a special kin…

Triangle Sum Conjecture

One method to create parallel lines

Triangle Third Angle Conjecture

SSS Conjecture

The sum of the measures of every triangle is 180 degrees.

By arrainging congruent triangles.

If two angles of one triangle are equal in measure to two ang…

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

Triangle Sum Conjecture

The sum of the measures of every triangle is 180 degrees.

One method to create parallel lines

By arrainging congruent triangles.

triangle

interior angle

exterior angle

corollary to a theorem

a polygon with 3 sides

(of a triangle) when the sides of a triangle are extended, th…

(of a triangle) when the sides of a triangle are extended, th…

a statement that can be proven easily using the theorem

triangle

a polygon with 3 sides

interior angle

(of a triangle) when the sides of a triangle are extended, th…

Congruent Polygons

Third Angles Theorem

Congruent Triangles

Side-Side-Side (SSS) Postulate

Have congruent corresponding parts - their matching sides and…

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

If all six parts, (angles and sides) are congruent then the t…

If three sides of one triangle are congruent to the three sid…

Congruent Polygons

Have congruent corresponding parts - their matching sides and…

Third Angles Theorem

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

Acute Triangle

Equiangular Triangle

Obtuse Triangle

Right Triangle

a triangle that has 3 acute angles

a triangle that has 3 congruent acute angles

a triangle that has 1 obtuse angle

a triangle that has 1 right angle

Acute Triangle

a triangle that has 3 acute angles

Equiangular Triangle

a triangle that has 3 congruent acute angles

Equilateral

Isosceles

Scalene

Pick any two sides... Set the equations e…

All three sides of triangle are congruent

At least two sides of triangle are congruent

No two sides of triangle are congruent

Find x and the length of each side of triangle RST is an equi…

Equilateral

All three sides of triangle are congruent

Isosceles

At least two sides of triangle are congruent

Symmetric Property

Reflexive Property

Transitive Property

Addition Postulate

If a = b, then b = a.

a is congruent/equal to a

If a = b and b = c, then a = c

If equal quantities are added to equal quantities, the sums a…

Symmetric Property

If a = b, then b = a.

Reflexive Property

a is congruent/equal to a

Angle Sum Theorem

exterior angle theorem

third angle theorem

Side Side Side

all the measures of a triangle equal 180

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

if 2 angles of one triangle are congruent to 2 angles of a 2n…

if the corresponding sides of two triangles are congruent con…

Angle Sum Theorem

all the measures of a triangle equal 180

exterior angle theorem

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

Congruent Triangles

Acute Triangle

Scalene Triangle

Right Triangle

Two triangles with all corresponding (matching up) sides cong…

A triangle with all acute angles.

A triangle with no sides congruent.

A triangle with a right angle.

Congruent Triangles

Two triangles with all corresponding (matching up) sides cong…

Acute Triangle

A triangle with all acute angles.

Disc

Isometric Paper

Right triangular Prism

Oblique Triangular Prism

A _____ is the set of all points on a circle and in the inter…

_________ is often used by artists and engineers to create th…

A triangle translated through space in a direction perpendicu…

When a triangle is translated through space in a direction th…

Disc

A _____ is the set of all points on a circle and in the inter…

Isometric Paper

_________ is often used by artists and engineers to create th…

Angle-Angle-Side (AAS) Theorem

Angle-Side-Angle (ASA) Postulate

Base angles of an isosceles triangle

Base of an isosceles triangle

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

If two triangles and the included angle of one triangle are c…

The congruent angles are called the _____.

The non-congruent side is called the ____ of the isosceles tr…

Angle-Angle-Side (AAS) Theorem

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

Angle-Side-Angle (ASA) Postulate

If two triangles and the included angle of one triangle are c…

AAS

ASA

Base Angles of an Isosceles Triangle

Base of an Isosceles Triangle

If 2 angles and a nonincluded side of one triangle are congru…

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

The 2 angles of an isosceles triangle that are not the vertex…

The third side of an isosceles triangle

AAS

If 2 angles and a nonincluded side of one triangle are congru…

ASA

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

Congruent Polygons

Corresponding Parts

Triangle Angel-Sum Theorem

SSS: side-side-side

polygons that have corresponding sides congruent and correspo…

...

If 2 angles of one triangle are congruent to two angles of an…

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

Congruent Polygons

polygons that have corresponding sides congruent and correspo…

Corresponding Parts

...

congruent figures

Third Angles Theorem

Side-Side-Side Postulate

Side-Angle-Side Postulate

figures that have the same size and shape

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

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 figures

figures that have the same size and shape

Third Angles Theorem

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

Acute Triangle

Equiangular Triangle

Obtuse Triangle

Right Triangle

A triangle in which all three angles have a measure of less t…

A triangle in which all three angles have a measure of 60 deg…

A triangle in which one of the angles has a measure greater t…

A triangle in which one of the angles has a measure of 90 deg…

Acute Triangle

A triangle in which all three angles have a measure of less t…

Equiangular Triangle

A triangle in which all three angles have a measure of 60 deg…