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

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

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…

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

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…

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

detour proofs

midpoint formula

perpendicular bisector

distance

proofs in which it is necessary to prove multiple pairs of tr…

used to find midpoints of segs...take the average of their en…

the line that bisects and is perpendicular to the segment

length of the shortest path between two objects

detour proofs

proofs in which it is necessary to prove multiple pairs of tr…

midpoint formula

used to find midpoints of segs...take the average of their en…

polygon

triangle

side

vertices

a shape with four or more sides

-a shape with three sides... -angles add up to 180 degrees

segment joining two consecutive vertices

-plural of vertex... -each angular point of a polygon

polygon

a shape with four or more sides

triangle

-a shape with three sides... -angles add up to 180 degrees

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)

classification by sides

classification by angles

Theorem 4.1 - Triangle Sum Theorem

Corollary to triangle sum theorem

equilateral... isosceles... scalene

acute... equilangular... right ... obtuse

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

the acute angles of a right triangle are complementary

classification by sides

equilateral... isosceles... scalene

classification by angles

acute... equilangular... right ... obtuse

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…

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…

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

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

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…

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 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…

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

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…

Angle sum theorem

Exterior angle

Interior Angles

Remote interior angles

the sum of the measures of the angles of a triangle is 180

an angle formed outside the triangle from an original side of…

angles inside the triangle

the two inside angles of a triangle that are nonadjacent to t…

Angle sum theorem

the sum of the measures of the angles of a triangle is 180

Exterior angle

an angle formed outside the triangle from an original side of…

congruent

congruent triangles

CPCTC

naming two congruent figures

-same size and shape

-are the same size and shape, the corresponding angles are co…

"corresponding parts of congruent triangles are congruent"

-the corresponding pieces must line up

congruent

-same size and shape

congruent triangles

-are the same size and shape, the corresponding angles are co…

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

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…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…

Acute triangle

Obtuse triangle

Right triangle

Congruent triangles

triangle with all 3 angles acute

triangle with one obtuse angle

triangle with 1 right angle

When two triangles are congruent they will have exactly the s…

Acute triangle

triangle with all 3 angles acute

Obtuse triangle

triangle with one obtuse angle

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

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

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

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…

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…

isos △ th

corollary 3

conv of isos △ th

median

if two sides of a triangles are congruent, then the angles op…

the bisector of the vertex angle of an isosceles triangle is…

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

a segment from a vertex of a triangle to the midpoint of the…

isos △ th

if two sides of a triangles are congruent, then the angles op…

corollary 3

the bisector of the vertex angle of an isosceles triangle is…

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

acute triangle

equiangular triangle

obtuse triangle

equilateral triangle

a triangle in which all of the angles are acute angles

a triangle with all angles congruent

a triangle with an obtuse angle

a triangle with all sides congruent

acute triangle

a triangle in which all of the angles are acute angles

equiangular triangle

a triangle with all angles congruent

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…

Third Angles Theorem

Angle Angle Side Theorem

Isosceles Triangle Theorem

Converse of the Isosceles Triangle The…

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

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

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

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

Third Angles Theorem

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

Angle Angle Side Theorem

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