# Study sets matching "honors geometry chapter 4"

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

Triangle Sum Theorem

Exterior Angle Theorem

Flow Proof

Corollary

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

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

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

A statement that follows directly from a theorem.

Triangle Sum Theorem

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

Exterior Angle Theorem

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

scalene

isosceles

47º

78º

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

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

m∠1=?

m∠2=?

scalene

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

isosceles

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

The sum of the measures of the interior…

The base angles of an isosceles triangl…

It is NOT possible for an obtuse triang…

An exterior angle of a triangle is NOT…

True!

True!

True!

True!

The sum of the measures of the interior…

True!

The base angles of an isosceles triangl…

True!

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

If two angles of one triangle are congr…

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 anoth…

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 congr…

the third angles are congruent

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

detour proofs

midpoint formula

perpendicular bisector

distance

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

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

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 tri…

midpoint formula

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

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 i…

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

The acute angles of a right triangle are complementary.

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

Triangle Sum Theorem (4.1)

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

Exterior Angle Theorem (4.1)

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

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 i…

the acute angles of a right triangle are complementary

classification by sides

equilateral... isosceles... scalene

classification by angles

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

congruent

SSS Postulate

SAS Postulate

ASA Postulate

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

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

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

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

congruent

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

SSS Postulate

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

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 Triangles

SSS Postulate

ASA Postulate

SAS Postulate

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

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

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

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

Congruent Triangles

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

SSS Postulate

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

Congruent polygons

3rd angle theorem

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

Polygon with congruent corresponding sides and congruent corre…

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

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

If 2 sides and an

**included angle**of one triangle are congrue…Congruent polygons

Polygon with congruent corresponding sides and congruent corre…

3rd angle theorem

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

Triangle

Polygon

Acute triangle

Obtuse triangle

A 3-sided polygon who's interior angles must equal 180 degrees.

A closed figure which is the union of line segments.

Triangle that is only made up of 3 acute angles (angles that h…

A triangle with only one obtuse angle and two other acute angl…

Triangle

A 3-sided polygon who's interior angles must equal 180 degrees.

Polygon

A closed figure which is the union of line segments.

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 p…

Corresponding parts of congruent triangles are congruent (inte…

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

Congruent figures

Figures hat have the same size and shape

Definition of congruent triangles

2 triangles are congruent IF AND ONLY IF their corresponding p…

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 figures

Definition of congruent triangles

CPCTC

Side-side-side postulate

Same size and shape

2 triangles are congruent iff their corresponding parts are co…

Corresponding parts of congruent triangles are congruent.

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

Congruent figures

Same size and shape

Definition of congruent triangles

2 triangles are congruent iff their corresponding parts are co…

Congruent polygons

Corollary

Legs of an isosceles triangle

Base of an isosceles triangle

_______have congruent corresponding parts--their matching side…

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 side…

Congruent polygons

_______have congruent corresponding parts--their matching side…

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 a…

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 congru…

Third Angle Theorem (TAT)

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

Side-side-side Postulate (SSS)

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

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 ano…

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

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 ano…

detour proof

Mid-point formula

Theorem (4.1)

Theorem (4.3)

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

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

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 o…

Mid-point formula

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