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Definitions, Postulates and Theorems

Name:

Definitions

Name

Definition

Visual Clue

Complementary

Two angles whose measures

 

Angles

have a sum of 90o

 

 

 

 

Supplementary

Two angles whose measures

 

Angles

have a sum of 180o

 

 

 

 

Theorem

A statement that can be proven

 

 

 

 

Vertical Angles

Two angles formed by intersecting lines and

 

 

facing in the opposite direction

 

Transversal

A line that intersects two lines in the same

 

 

plane at different points

 

 

 

 

Corresponding

Pairs of angles formed by two lines and a

 

angles

transversal that make an F pattern

 

Same-side interior

Pairs of angles formed by two lines and a

 

angles

transversal that make a C pattern

 

Alternate interior

Pairs of angles formed by two lines and a

 

angles

transversal that make a Z pattern

 

Congruent triangles

Triangles in which corresponding parts (sides

 

 

and angles) are equal in measure

 

 

 

 

Similar triangles

Triangles in which corresponding angles are

 

 

equal in measure and corresponding sides are

 

 

in proportion (ratios equal)

 

Angle bisector

A ray that begins at the vertex of an angle and

 

 

divides the angle into two angles of equal

 

 

measure

 

Segment bisector

A ray, line or segment that divides a segment

 

 

into two parts of equal measure

 

Legs of an

The sides of equal measure in an isosceles

 

isosceles triangle

triangle

 

 

 

 

Base of an

The third side of an isosceles triangle

 

isosceles triangle

 

 

Equiangular

Having angles that are all equal in measure

 

 

 

 

Perpendicular

A line that bisects a segment and is

 

bisector

perpendicular to it

 

Altitude

A segment from a vertex of a triangle

 

 

perpendicular to the line containing the

 

 

opposite side

 

Page 1 of 11

Definitions, Postulates and Theorems

Definitions

Name

 

Definition

 

 

 

Visual Clue

 

Geometric mean

 

The value of x in proportion

 

 

 

 

 

 

a/x = x/b where a, b, and x are positive

 

 

 

 

numbers (x is the geometric mean between a

 

 

 

 

and b)

 

 

 

 

 

Sine, sin

 

For an acute angle of a right triangle, the ratio

 

 

 

 

of the side opposite the angle to the measure

 

 

 

 

of the hypotenuse. (opp/hyp)

 

 

 

 

Cosine, cos

 

For an acute angle of a right triangle the ratio

 

 

 

 

of the side adjacent to the angle to the measure

 

 

 

 

of the hypotenuse. (adj/hyp)

 

 

 

 

Tangent, tan

 

For an acute angle of a right triangle, the ratio

 

 

 

 

of the side opposite to the angle to the measure

 

 

 

 

of the side adjacent (opp/adj)

 

 

 

 

 

 

 

 

 

 

 

 

Algebra Postulates

 

 

 

 

 

 

 

Name

 

Definition

 

 

 

Visual Clue

 

Addition Prop. Of

 

If the same number is added to equal

 

 

 

equality

 

numbers, then the sums are equal

 

 

Subtraction Prop. Of

 

If the same number is subtracted from equal

 

 

equality

 

numbers, then the differences are equal

 

 

Multiplication Prop.

 

If equal numbers are multiplied by the same

 

 

Of equality

 

number, then the products are equal

 

 

 

 

 

 

 

 

Division Prop. Of

 

If equal numbers are divided by the same

 

 

equality

 

number, then the quotients are equal

 

 

Reflexive Prop. Of

 

A number is equal to itself

 

 

 

 

equality

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Symmetric Property

 

If a = b then b = a

 

 

 

 

of Equality

 

 

 

 

 

 

 

Substitution Prop. Of

 

If values are equal, then one value may be

 

 

equality

 

substituted for the other.

 

 

 

 

 

 

 

 

 

 

 

Transitive Property of

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

 

 

 

 

Equality

 

 

 

 

 

 

 

Distributive Property

 

a(b + c) = ab + ac

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Congruence Postulates

 

 

 

 

 

Name

 

 

Definition

 

 

Visual Clue

 

Reflexive Property of Congruence

A ≅ A

 

 

 

 

Symmetric Property of

If A ≅ B,then

B ≅ A

 

 

 

Congruence

 

 

 

 

 

 

 

Transitive Property of Congruence

If A ≅ B and B ≅ C then

 

 

 

 

 

 

 

A ≅ C

 

 

 

 

Page 2 of 11

Definitions, Postulates and Theorems

Angle Postulates And Theorems

Name

Definition

Visual Clue

Angle Addition

For any angle, the measure of the whole is

 

postulate

equal to the sum of the measures of its non-

 

 

overlapping parts

 

Linear Pair Theorem

If two angles form a linear pair, then they

 

 

are supplementary.

 

Congruent

If two angles are supplements of the same

 

supplements theorem

angle, then they are congruent.

 

Congruent

If two angles are complements of the same

 

complements

angle, then they are congruent.

 

theorem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Right Angle

All right angles are congruent.

 

Congruence

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vertical Angles

Vertical angles are equal in measure

 

Theorem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

If two congruent angles are supplementary,

 

 

then each is a right angle.

 

Angle Bisector

If a point is on the bisector of an angle, then

 

Theorem

it is equidistant from the sides of the angle.

 

Converse of the

If a point in the interior of an angle is

 

Angle Bisector

equidistant from the sides of the angle, then

 

Theorem

it is on the bisector of the angle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lines Postulates And Theorems

 

Name

 

Definition

Visual Clue

Segment Addition

 

For any segment, the measure of the whole

 

postulate

 

is equal to the sum of the measures of its

 

 

 

non-overlapping parts

 

Postulate

 

Through any two points there is exactly

 

 

 

one line

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Postulate

 

If two lines intersect, then they intersect at

 

 

 

exactly one point.

 

Common Segments

 

Given collinear points A,B,C and D

 

Theorem

 

arranged as shown, if

 

 

 

≅

 

 

 

then

 

 

A

B

C

D

 

 

 

 

 

 

 

 

≅

 

 

 

 

 

 

 

 

 

A

 

C

B

C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Corresponding Angles

 

If two parallel lines are intersected by a

 

Postulate

 

transversal, then the corresponding angles

 

 

 

are equal in measure

 

Converse of

 

If two lines are intersected by a transversal

 

Corresponding Angles

 

and corresponding angles are equal in

 

Postulate

 

measure, then the lines are parallel

 

Page 3 of 11

Definitions, Postulates and Theorems

Lines Postulates And Theorems

Name

Definition

Visual Clue

Postulate

Through a point not on a given line, there

 

 

is one and only one line parallel to the

 

 

given line

 

Alternate Interior

If two parallel lines are intersected by a

 

Angles Theorem

transversal, then alternate interior angles

 

 

are equal in measure

 

Alternate Exterior

If two parallel lines are intersected by a

 

Angles Theorem

transversal, then alternate exterior angles

 

 

are equal in measure

 

Same-side Interior

If two parallel lines are intersected by a

 

Angles Theorem

transversal, then same-side interior angles

 

 

are supplementary.

 

Converse of Alternate

If two lines are intersected by a transversal

 

Interior Angles

and alternate interior angles are equal in

 

Theorem

measure, then the lines are parallel

 

Converse of Alternate

If two lines are intersected by a transversal

 

Exterior Angles

and alternate exterior angles are equal in

 

Theorem

measure, then the lines are parallel

 

Converse of Same-side

If two lines are intersected by a transversal

 

Interior Angles

and same-side interior angles are

 

Theorem

supplementary, then the lines are parallel

 

Theorem

If two intersecting lines form a linear pair

 

 

of congruent angles, then the lines are

 

 

perpendicular

 

Theorem

If two lines are perpendicular to the same

 

 

transversal, then they are parallel

 

 

 

 

Perpendicular

If a transversal is perpendicular to one of

 

Transversal Theorem

two parallel lines, then it is perpendicular

 

 

to the other one.

 

 

 

 

Perpendicular Bisector

If a point is on the perpendicular bisector

 

Theorem

of a segment, then it is equidistant from

 

 

the endpoints of the segment

 

Converse of the

If a point is the same distance from both

 

Perpendicular Bisector

the endpoints of a segment, then it lies on

 

Theorem

the perpendicular bisector of the segment

 

Parallel Lines Theorem

In a coordinate plane, two nonvertical

 

 

lines are parallel IFF they have the same

 

 

slope.

 

Perpendicular Lines

In a coordinate plane, two nonvertical

 

Theorem

lines are perpendicular IFF the product of

 

 

their slopes is -1.

 

Two-Transversals

If three or more parallel lines intersect two

 

Proportionality

transversals, then they divide the

 

Corollary

transversals proportionally.

 

Page 4 of 11

Definitions, Postulates and Theorems

Triangle Postulates And Theorems

Name

Definition

Visual Clue

Angle-Angle

If two angles of one triangle are equal in measure

 

(AA)

to two angles of another triangle, then the two

 

Similarity

triangles are similar

 

Postulate

 

 

Side-side-side

If the three sides of one triangle are proportional to

 

(SSS)

the three corresponding sides of another triangle,

 

Similarity

then the triangles are similar.

 

Theorem

 

 

Side-angle-

If two sides of one triangle are proportional to two

 

side SAS)

sides of another triangle and their included angles

 

Similarity

are congruent, then the triangles are similar.

 

Theorem

 

 

Third Angles

If two angles of one triangle are congruent to two

 

Theorem

angles of another triangle, then the third pair of

 

 

angles are congruent

 

Side-Angle-

If two sides and the included angle of one triangle

 

Side

are equal in measure to the corresponding sides

 

Congruence

and angle of another triangle, then the triangles are

 

Postulate

congruent.

 

SAS

 

 

Side-side-side

If three sides of one triangle are equal in measure

 

Congruence

to the corresponding sides of another triangle, then

 

Postulate

the triangles are congruent

 

SSS

 

 

Angle-side-

If two angles and the included side of one triangle

 

angle

are congruent to two angles and the included side

 

Congruence

of another triangle, then the triangles are

 

Postulate

congruent.

 

ASA

 

 

Triangle Sum

The sum of the measure of the angles of a triangle

 

Theorem

is 180o

 

Corollary

The acute angles of a right triangle are

 

 

complementary.

 

Exterior angle

An exterior angle of a triangle is equal in measure

 

theorem

to the sum of the measures of its two remote

 

 

interior angles.

 

Triangle

If a line parallel to a side of a triangle intersects the

 

Proportionality

other two sides, then it divides those sides

 

Theorem

proportionally.

 

Converse of

If a line divides two sides of a triangle

 

Triangle

proportionally, then it is parallel to the third side.

 

Proportionality

 

 

Theorem

 

 

Page 5 of 11

Definitions, Postulates and Theorems

Triangle Postulates And Theorems

Name

Definition

Visual Clue

Triangle Angle

An angle bisector of a triangle divides the opposite

 

Bisector

sides into two segments whose lengths are

 

Theorem

proportional to the lengths of the other two sides.

 

 

 

 

Angle-angle-

If two angles and a non-included side of one

 

side

triangle are equal in measure to the corresponding

 

Congruence

angles and side of another triangle, then the

 

Theorem

triangles are congruent.

 

AAS

 

 

Hypotenuse-

If the hypotenuse and a leg of a right triangle are

 

Leg

congruent to the hypotenuse and a leg of another

 

Congruence

right triangle, then the triangles are congruent.

 

Theorem

 

 

HL

 

 

Isosceles

If two sides of a triangle are equal in measure, then

 

triangle

the angles opposite those sides are equal in

 

theorem

measure

 

Converse of

If two angles of a triangle are equal in measure,

 

Isosceles

then the sides opposite those angles are equal in

 

triangle

measure

 

theorem

 

 

Corollary

If a triangle is equilateral, then it is equiangular

 

 

 

 

Corollary

The measure of each angle of an equiangular

 

 

triangle is 60o

 

Corollary

If a triangle is equiangular, then it is also

 

 

equilateral

 

Theorem

If the altitude is drawn to the hypotenuse of a right

 

 

triangle, then the two triangles formed are similar

 

 

to the original triangle and to each other.

 

Pythagorean

In any right triangle, the square of the length of the

 

theorem

hypotenuse is equal to the sum of the square of the

 

 

lengths of the legs.

 

Geometric

The length of the altitude to the hypotenuse of a

 

Means

right triangle is the geometric mean of the lengths

 

Corollary a

of the two segments of the hypotenuse.

 

Geometric

The length of a leg of a right triangle is the

 

Means

geometric mean of the lengths of the hypotenuse

 

Corollary b

and the segment of the hypotenuse adjacent to that

 

 

leg.

 

Circumcenter

The circumcenter of a triangle is equidistant from

 

Theorem

the vertices of the triangle.

 

 

 

 

Incenter

The incenter of a triangle is equidistant from the

 

Theorem

sides of the triangle.

 

 

 

 

Page 6 of 11

Definitions, Postulates and Theorems

Triangle Postulates And Theorems

Name

Definition

 

 

 

 

Visual Clue

Centriod

The centriod of a triangle is located 2/3 of the

 

Theorem

distance from each vertex to the midpoint of the

 

 

opposite side.

 

Triangle

A midsegment of a triangle is parallel to a side of

 

Midsegment

triangle, and its length is half the length of that

 

Theorem

side.

 

 

 

 

 

 

 

Theorem

If two sides of a triangle are not congruent, then

 

 

the larger angle is opposite the longer side.

 

 

 

 

 

 

 

 

 

 

Theorem

If two angles of a triangle are not congruent, then

 

 

the longer side is opposite the larger angle.

 

 

 

 

 

 

 

 

 

 

Triangle

The sum of any two side lengths of a triangle is

 

Inequality

greater than the third side length.

 

Theorem

 

 

 

 

 

 

 

 

 

 

Hinge

If two sides of one triangle are congruent to two

 

Theorem

sides of another triangle and the third sides are not

 

 

congruent, then the longer third side is across from

 

 

the larger included angle.

 

Converse of

If two sides of one triangle are congruent to two

 

Hinge

sides of another triangle and the third sides are not

 

Theorem

congruent, then the larger included angle is across

 

 

from the longer third side.

 

Converse of

If the sum of the squares of the lengths of two

 

the

sides of a triangle is equal to the square of the

 

Pythagorean

length of the third side, then the triangle is a right

 

Theorem

triangle.

 

 

 

 

 

Pythagorean

In ∆ABC, c is the length of the longest side. If c² >

 

Inequalities

a² + b², then ∆ABC is an obtuse triangle. If c² < a²

 

Theorem

+ b², then ∆ABC is acute.

 

 

 

 

 

 

 

 

 

 

45Ëš-45Ëš-90Ëš

In a 45Ëš-45Ëš-90Ëš triangle, both legs are congruent,

 

Triangle

and the length of the hypotenuse is the length of a

 

Theorem

length times the square root of 2.

 

 

 

 

 

 

 

 

 

 

30Ëš-60Ëš-90Ëš

In a 30Ëš-60Ëš-90Ëš triangle, the length of the

 

Triangle

hypotenuse is 2 times the length of the shorter leg,

 

Theorem

and the length of the longer leg is the length of the

 

 

shorter leg times the square root of 3.

 

Law of Sines

For any triangle ABC with side lengths a, b, and c,

 

 

 

sin A

=

sin B

=

sin C

 

 

 

 

a

 

b

 

 

c

 

Law of

For any triangle, ABC with sides a, b, and c,

 

Cosines

a2 =b2

+c2

-2bc cos A,b2 = a2 +c2 -2ac cos B,

 

 

c2 = a2

 

+b2

-2ac cosC

 

Page 7 of 11

 

 

 

Definitions, Postulates and Theorems

 

Plane Postulates And Theorems

 

Name

 

Definition

Visual Clue

Postulate

 

Through any three noncollinear points there is exactly

 

 

 

one plane containing them.

 

 

 

 

 

 

Postulate

 

If two points lie in a plane, then the line containing those

 

 

 

points lies in the plane

 

Postulate

 

If two points lie in a plane, then the line containing those

 

 

 

points lies in the plane

 

 

 

 

 

Polygon Postulates And Theorems

 

Name

 

Definition

Visual Clue

Polygon Angle

The sum of the interior angle measures of a

 

Sum Theorem

convex polygon with n sides.

 

Polygon Exterior

The sum of the exterior angle measures, one

 

Angle Sum

 

angle at each vertex, of a convex polygon is

 

Theorem

 

360Ëš.

 

Theorem

 

If a quadrilateral is a parallelogram, then its

 

 

 

 

opposite sides are congruent.

 

Theorem

 

If a quadrilateral is a parallelogram, then its

 

 

 

 

opposite angles are congruent.

 

Theorem

 

If a quadrilateral is a parallelogram, then its

 

 

 

 

consecutive angles are supplementary.

 

Theorem

 

If a quadrilateral is a parallelogram, then its

 

 

 

 

diagonals bisect each other.

 

Theorem

 

If one pair of opposite sides of a quadrilateral are

 

 

 

 

parallel and congruent, then the quadrilateral is a

 

 

 

 

parallelogram.

 

Theorem

 

If both pairs of opposite sides of a quadrilateral

 

 

 

 

are congruent, then the quadrilateral is a

 

 

 

 

parallelogram.

 

Theorem

 

If both pairs of opposite angles are congruent,

 

 

 

 

then the quadrilateral is a parallelogram.

 

Theorem

 

If an angle of a quadrilateral is supplementary to

 

 

 

 

both of its consecutive angles, then the

 

 

 

 

quadrilateral is a parallelogram.

 

Theorem

 

If the diagonals of a quadrilateral bisect each

 

 

 

 

other, then the quadrilateral is a parallelogram.

 

 

 

 

 

Theorem

 

If a quadrilateral is a rectangle, then it is a

 

 

 

 

parallelogram.

 

 

 

 

 

Theorem

 

If a parallelogram is a rectangle, then its

 

 

 

 

diagonals are congruent.

 

 

 

 

 

Theorem

 

If a quadrilateral is a rhombus, then it is a

 

 

 

 

parallelogram.

 

 

 

 

 

 

Page 8 of 11

Definitions, Postulates and Theorems

Polygon Postulates And Theorems

Name

Definition

Visual Clue

Theorem

If a parallelogram is a rhombus then its

 

 

diagonals are perpendicular.

 

 

 

 

Theorem

If a parallelogram is a rhombus, then each

 

 

diagonal bisects a pair of opposite angles.

 

 

 

 

Theorem

If one angle of a parallelogram is a right angle,

 

 

then the parallelogram is a rectangle.

 

 

 

 

Theorem

If the diagonals of a parallelogram are

 

 

congruent, then the parallelogram is a rectangle.

 

 

 

 

Theorem

If one pair of consecutive sides of a

 

 

parallelogram are congruent, then the

 

 

parallelogram is a rhombus.

 

 

 

 

Theorem

If the diagonals of a parallelogram are

 

 

perpendicular, then the parallelogram is a

 

 

rhombus.

 

 

 

 

Theorem

If one diagonal of a parallelogram bisects a pair

 

 

of opposite angles, then the parallelogram is a

 

 

rhombus.

 

 

 

 

Theorem

If a quadrilateral is a kite then its diagonals are

 

 

perpendicular.

 

 

 

 

Theorem

If a quadrilateral is a kite then exactly one pair

 

 

of opposite angles are congruent.

 

 

 

 

Theorem

If a quadrilateral is an isosceles trapezoid, then

 

 

each pair of base angles are congruent.

 

 

 

 

Theorem

If a trapezoid has one pair of congruent base

 

 

angles, then the trapezoid is isosceles.

 

 

 

 

Theorem

A trapezoid is isosceles if and only if its

 

 

diagonals are congruent.

 

 

 

 

Trapezoid

The midsegment of a trapezoid is parallel to

 

Midsegment

each base, and its length is one half the sum of

 

Theorem

the lengths of the bases.

 

Page 9 of 11

Definitions, Postulates and Theorems

Polygon Postulates And Theorems

Name

 

Definition

 

 

 

 

 

 

 

 

 

 

Visual Clue

 

Proportional

 

If the similarity ratio of two similar figures is

a

,

 

 

Perimeters and

 

 

 

 

 

 

b

 

 

Areas Theorem

 

then the ratio of their perimeter is

a

and the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

ratio of their areas is

a2

a

2

 

 

 

 

 

 

 

or

 

 

 

 

 

 

 

 

 

b2

 

 

 

 

 

 

 

 

b

 

 

 

 

Area Addition

 

The area of a region is equal to the sum of the

 

 

 

Postulate

 

areas of its nonoverlapping parts.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Circle Postulates And Theorems

 

 

 

 

 

 

 

 

 

 

 

 

Name

 

Definition

 

 

 

 

 

 

 

 

 

 

Visual Clue

 

Theorem

 

If a line is tangent to a circle, then it is perpendicular

 

 

 

 

to the radius drawn to the point of tangency.

 

 

 

Theorem

 

If a line is perpendicular to a radius of a circle at a

 

 

 

 

 

point on the circle, then the line is tangent to the

 

 

 

 

 

circle.

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

 

If two segments are tangent to a circle from the

 

 

 

 

 

same external point then the segments are

 

 

 

 

 

congruent.

 

 

 

 

 

 

 

 

 

 

 

 

Arc Addition

 

The measure of an arc formed by two adjacent arcs

 

 

 

Postulate

 

is the sum of the measures of the two arcs.

 

 

 

Theorem

 

In a circle or congruent circles: congruent central

 

 

 

 

 

angles have congruent chords, congruent chords

 

 

 

 

 

have congruent arcs and congruent acrs have

 

 

 

 

 

congruent central angles.

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

 

In a circle, if a radius (or diameter) is perpendicular

 

 

 

 

 

to a chord, then it bisects the chord and its arc.

 

 

 

 

 

 

 

 

Theorem

 

In a circle, the perpendicular bisector of a chord is a

 

 

 

 

radius (or diameter).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Inscribed

 

The measure of an inscribed angle is half the

 

 

 

Angle

 

measure of its intercepted arc.

 

 

 

 

 

 

 

 

Theorem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Corollary

 

If inscribed angles of a circle intercept the same arc

 

 

 

 

 

or are subtended by the same chord or arc, then the

 

 

 

 

 

angles are congruent

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

 

An inscribed angle subtends a semicircle IFF the

 

 

 

 

 

angle is a right angle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Theorem

 

If a quadrilateral is inscribed in a circle, then its

 

 

 

 

 

opposite angles are supplementary.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Page 10 of 11

Definitions, Postulates and Theorems

Circle Postulates And Theorems

Name

Definition

 

 

Visual Clue

 

Theorem

If a tangent and a secant (or chord) intersect on a

 

 

 

 

circle at the point of tangency, then the measure of

 

 

 

 

the angle formed is half the measure of its

 

 

 

 

intercepted arc.

 

 

 

 

Theorem

If two secants or chords intersect in the interior of a

 

 

 

 

circle, then the measure of each angle formed is half

 

 

 

 

the sum of the measures of the intercepted arcs.

 

 

 

Theorem

If a tangent and a secant, two tangents or two

 

 

 

 

secants intersect in the exterior of a circle, then the

 

 

 

 

measure of the angle formed is half the difference of

 

 

 

 

the measure of its intercepted arc.

 

 

 

Chord-Chord

If two chords intersect in the interior of a circle,

 

 

 

Product

then the products of the lengths of the segments of

 

 

 

Theorem

the chords are equal.

 

 

 

 

Secant-

If two secants intersect in the exterior of a circle,

 

 

 

Secant

then the product of the lengths of one secant

 

 

 

Product

segment and its external segment equals the product

 

 

 

Theorem

of the lengths of the other secant segment and its

 

 

 

 

external segment.

 

 

 

 

Secant-

If a secant and a tangent intersect in the exterior of a

 

 

 

Tangent

circle, then the product of the lengths of the secant

 

 

 

Product

segment and its external segment equals the length

 

 

 

Theorem

of the tangent segment squared.

 

 

 

Equation of a

The equal of a circle with center (h, k) and radius r

 

 

 

Circle

is (x – h)2 + (y – k)2

= r2

 

 

 

 

 

 

 

 

 

 

Other

 

 

 

 

 

 

Name

 

Definition

 

 

Visual Clue

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Page 11 of 11