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87 Cards in this Set
 Front
 Back
If a point is on the perpendicular bisector of a segment then

the point is equidistant from both endpoints of the segment


If a point is equidistant from both endpoints on segment then

it is on the perpendicular bisector


If a point is on the bisector of and angle then

it is equidistant from the two sides of the angle


The Perpendicular bisector s of a triangle intersect at a point that is

equidistant from the vertices of the triangle


The angle bisectors of a triangle intersect at a point that is

equidistant form the sides of the triangle.


The Medians of a triangle intersect at a point that is

two thirds of the distance from each vertex to the midpoint of the opposite side


The lines containing the altitudes of a triangle are

congruent


The segment connecting the midpoints of two sides of a triangle

is parallel to the third side and half as long.


If one side of a triangle is longer than another side then

the angle opposite of the longer side is larger than the angle opposite the shorter side


If one angle is larger than another angle the segment opposite the larger angle is

larger than the segment opposite the smaller angle.


The measure of an exterior angle of a triangle is greater than the measure of

the two nonadjacent interior angles


The Sum of the lengths of any two sides of a triangle is greater than

the length of the third side


If two sides of one triangle are congruent to two sides of another triangle and the included angle of the second and the third side of the first

is longer than the third side of the second


If two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third of the second

then the included angle of the first is larger than the included angle of the second


Polygon is a plane figure that meets the following conditions

It is formed by three or more segments called sides
Each sides intersects with exactly two other sides 

Each endpoint in a polygon is a

Vertex


Equilateral means all sides are

Congruent


Equiangular means all angles are

Congruent


Regular means that a polygon is both

equilateral and equiangular


Parallelograms are quadrilaterals that have

2 pairs of parallel sides


Parallelograms opposite sides are

Congruent


Parallelograms opposite angles are

Congruent


Parallelograms consecutive angles are

supplementary


Parallelograms diagonals

bisect each other


Rhombuses are

Parallelograms with 4 congruent sides


Rectangles are

Parallelograms with 4 right angles


Squares are

are Parallelograms with4 congruent sides and 4 right angles


A Parallelogram is a rhombus if and only if

it’s diagonals are perpendicular


A Parallelogram is a rhombus if and only if

if each diagonal bisects a pair of opposite angles


A Parallelogram is a rectangle if and only if

its diagonals are congruent


If a trapezoid is isosceles then

each pair of base angles is congruent


If a trapezoid has a pair of congruent base angles then

it is an isosceles trapezoid


A trapezoid is isosceles if and only if

it’s diagonals are congruent


The Midsegment of a trapezoid is parallel to

each base and is half of the sum of the bases lengths.


If a quadrilateral is a kite then

its diagonals are perpendicular


If a quadrilateral is a kite then

exactly one pair of opposite angles are congruent


The area of a square is

a side squared


If two polygons are congruent then they

have the same area


Area of a rectangle=

base times height


Area of a parallelogram is

base times height


The area of a triangle is

½ base times height


The area of a trapezoid is

½ h(b1+b2)


The area of a kite is

½ the product of the diagonals


The area of a Rhombus is

½ the product of the diagonals


Ratio a to b is written as

a/b or a:b


In a ration the quotient cannot be

zero


a/b=c/d then

ad=bc
b/a=d/c a and d are extremes b and c are means 

If two polygons are similar then the ratio between their perimeters is

equal to their corresponding sides


If two polygons are similar then their angles

are the same


Angle angle postulate

If two angles of one triangle are congruent to two angles of another triangle then the two triangles are similar.


SIDE SIDE SIDE Postulate

If the lengths of two triangles are proportional then the triangles are similar.


Side angle Side Postulate

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional then the triangles are similar.


If a line parallel to one side of a triangle intersects the other two sides then

it divides the two sides proportionally


If three lines intersect two transversals then

they divide the transversals proportionally


If a ray bisects an angle of a triangle then

it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.


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


In a right triangle the altitude from the right angle divides the hypotenuse into two segments. What is the geometric mean

The geometric mean of these two segments is the length of the altitude.


In a right Triangle the square of the length of the hypotenuse is equal to

the sum of the squares of the lengths of the legs.


If the square of the hypotenuse is less than the sum of the squares of the other two sides then

the triangle is acute


If the square of the hypotenuse is greater than the sum of the squares of the other two sides then

the triangle is obtuse


In a 45 45 90 tiangle the hypotenuse is

√2 times as long as each leg


In a 60 30 90 the hypotenuse and longer leg is

2 times as long as the shorter leg and the longer leg is √3 times as long as the shorter leg


If sinA =x then

sin1x =m angle A


If tanA =x then

tan1x =m angle A


If cosA =x then

cos1x =m angle A


casdf

asdfasdf


Center:

The exact middle of a circle


Radius

The distance from the circle to the center. If 2 circles have the same radius then they are congruent


Diameter

The distance across the circle through the center. It equals 2 times the radius.


Chord

A segment whose endpoints are points on the circle.


Secant

A line that intersects a circle in two points


Tangent

a line that intersects with the circle at just one point


Minor arcs

<180


Major arcs

>180


Semicircles

=180


If an angle is inscribed in a circle then its measure is

half the measure of its intercepted arc.


If two inscribed angles of a circle intercept the same arc then the angles

are congruent


If a right triangle is inscribed in a circle then the hypotenuse is

is a diameter of the circle


A quadrilateral can be inscribed in a circle if and only if its

opposite angles are supplementary.


If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is

one half the measure of its intercepted arc


If two chords intersect in the interior of a circle then the product of the lengths of the segments of one chord is equal to

the product of the lengths of the segments of the other chord


If two secant segments share the same endpoint outside a circle then the product of the length of one secant segment and the length of its external segment equals

the product of the length of the other secant segment and the length of its external segment.


If a secant segment and a tangent segment share an endpoint outside a circle then the product of the lengths of the secant segment and the lengths of its external segment equals

the square of the length of the tangent segment.


The circumference of a circle is

is c=pi D or 2 pi r


In a circle the ration of the length of a given arc to the circumference is equal to the

ration of the measure of the arc to 360


The Area of a circle is

pi time the square of the radius


The ratio of the area of a sector of a circle to the area of the circle is equal to the measure of

the intercepted arc to 360.
