#### Study sets matching "geometry chapter 4"

#### Study sets matching "geometry chapter 4"

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

Equiangular Triangle

A triangle with three congruent sides.

A triangle with at least two congruent sides.

A triangle with no sides congruent.

A triangle with three congruent angles.

Equilateral Triangle

A triangle with three congruent sides.

Isosceles Triangle

A triangle with at least two 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

SSS Theorem

ASA Postulate

AAS Postulate

SAS Postulate

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

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

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

If the 2 sides and the included angle of one triangle is cong…

SSS Theorem

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

ASA Postulate

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

Congruent Polygons

Third Angles Theorem

SSS (Side Side Side)

SAS (Side Angle Side)

Have congruent corresponding parts, their matching sides and…

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 of one tr…

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…

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

congruent polygons

SSS Postulate

SAS postulate

ASA postulate

polygons whose vertices can be matched up so that the corresp…

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

If two sides ad the included angle of one triangle are congru…

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

congruent polygons

polygons whose vertices can be matched up so that the corresp…

SSS Postulate

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

obtuse triangle

right triangle

acute triangle

scalene triangle

A triangle with one obtuse angle

A triangle with one right angle

A triangle with 3 acute angles

A triangle with no congruent sides

obtuse triangle

A triangle with one obtuse angle

right triangle

A triangle with one right angle

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…

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

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.

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

base

base angles

betweenness

congruence

The bottom side of a triangle. In an isosceles triangle with…

The angles at the base of a triangle. (p196)

Given 3 points P, Q, and R, if PQ + QR = PR, then Q is betwee…

Two figures are congruent if they have the same shape and siz…

base

The bottom side of a triangle. In an isosceles triangle with…

base angles

The angles at the base of a triangle. (p196)

CPCTC

Two polygons are congruent

Two triangles are congruent

SSS postulate

Corresponding parts of congruent triangles are congruent

if and only if their vertices can be matched up so that their…

If and only if their vertices can be matched up so that the c…

if side, side, side are congruent to another sss of a triagle…

CPCTC

Corresponding parts of congruent triangles are congruent

Two polygons are congruent

if and only if their vertices can be matched up so that their…

If three sides in a triangle are congr…

If two sides and an included angle in…

If two angles and an included side in…

If two angles and a side that is not i…

SSS (Side Side Side)

SAS (Side Angle Side)

ASA (Angle Side Angle)

AAS (Angle Angle Side) Theorem

If three sides in a triangle are congr…

SSS (Side Side Side)

If two sides and an included angle in…

SAS (Side Angle Side)

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

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…

Polygon Congruence Postulate

SSS Congruence Postulate

SAS Congruence Postulate

ASA Congruence Postulate

Two polygons are congruent if and only if... 1. the correspondin…

Polygon Congruence Postulate

Two polygons are congruent if and only if... 1. the correspondin…

SSS Congruence Postulate

congruent figures

definition of congruent triangles

postulate 12: SSS Postulate

postulate 13: SAS Postulate

figures that have the same shape and size

two triangles are congruent iff their corresponding parts are…

if three sides in one triangle are congruent to three sides i…

if two sides and an included angle of one triangle are congru…

congruent figures

figures that have the same shape and size

definition of congruent triangles

two triangles are congruent iff their corresponding parts are…

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…

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

coplanar

distance

noncoplanar

opposite reciprocals

Points, lines, segments, and so forth that lie in the same pl…

The length of the shortest path joining them.

Points, line, segments, and so forth that do not lie in the s…

Two numbers whose product is -1.

coplanar

Points, lines, segments, and so forth that lie in the same pl…

distance

The length of the shortest path joining them.

acute triangle

equiangular triangle

obtuse triangle

right triangle

a triangle with 3 acute angles

a triangle with three congruent angles

a triangle with one obtuse angle

a triangle with one right angle

acute triangle

a triangle with 3 acute angles

equiangular triangle

a triangle with three congruent angles

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?

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…

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

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

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…

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

...

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…

congruent figures

SSS

SAS

ASA

two figures that have the same size and shape

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 figures

two figures that have the same size and shape

SSS

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

Isosceles Triangle Theorem

Perpendicular Bisector

Median of a Triangle

Centroid

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

a segment that is perpendicular to another segment and bisect…

a segment whose endpoint are a vertex and the midpoint of the…

points where all the medians intersect

Isosceles Triangle Theorem

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

Perpendicular Bisector

a segment that is perpendicular to another segment and bisect…

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

Equiangular Triangle

A triangle with three congruent sides

A triangle with two congruent sides

A triangle with no congruent sides

A triangle with three congruent angles

Equilateral Triangle

A triangle with three congruent sides

Isosceles Triangle

A triangle with two congruent sides

congruent polygons

SSS Postulate

SAS Postulate

ASA Postulate

have congruent corresponding parts

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

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

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

congruent polygons

have congruent corresponding parts

SSS Postulate

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