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87 Cards in this Set

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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
sin-1x =m angle A
If tanA =x then
tan-1x =m angle A
If cosA =x then
cos-1x =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.