Final Exam Conjecture

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Conjectures

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Tangent Conjecture
A tangent to a circle is perpendicular to the radius drawn to the point of tangency
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Chord Arcs Conjecture
2 chords in a circle are congruent then their intercepted arcs are congruent
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Chord Central Angles Conjecture
if 2 chords in a circle are congruent then they determine 2 central angles that are congruent
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Perpendicular chord conjecture
The perpendicular from the center of a circle to the chord is the bisector of the chord
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Perpendicular Bisector of a chord conjecture
The perpendicular bisector of a chord passes through the center of a circle (diameter)
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Chord distance to center conjecture
2 congruent chords in a circle are equidistant from the center of the circle
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Inscribed Angle Conjecture
measure of an angle inscribed in the circle is the measure of the intercepted arc
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Inscribed angles intercepting arcs conjecture
Inscribed angles that intercept the same arc are congruent
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Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are supplementary
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Parallel lines intercepted arcs conjecture
Parallel lines intercept congruent arcs on a circle
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Circumference conjecture
if C is the circumference and d is the diameter of a circle then there is a number pi such that c\=pi x d. if d \= 2r, where r is the radius, then c \= 2 x pi x r
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Arc length conjecture
the length go an arc \= the measure of the arc divided by 360 degrees times the circumference
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Rectangle area conjecture
area of a rectangle is given by the formula, A\=bh, where A is the area, b is the length of the base, h is the height of the rectangle
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Parallelogram Area Conjecture
Area of parallelogram is given by formula A\=bh, where A is the area, b is the length of the base, and h is the height of parallelogram
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Triangle area conjecture
area of a triangle is given by the formula A\=1/2 bh where A is the area, b is the length of the base, and h is the height of the triangle
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Kite area conjecture
Area of a kite is given by the formula A\= 1/2 d1 d2, where d1 and d2 are the lengths of the diagonals
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Trapezoid Area Conjecture
Area of trapezoid is given by the formula A\=1/2 (b1+b2)h, where A is the area, b1 and b2 are the lengths of the 2 bases and h is the height of the trapezoid
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Regular Polygon Area
The area of a regular polygon is given by the formula A\=1/2 ask or A\=1/2ap, where A is the area, p is the perimeter, a is the apothem, s is the length of each side and n is the number of sides
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Circle area Conjecture
The area of a circle is given by the formula A\=∏r^2, were A is the area and r is the radius of the circle.
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Sector of a circle
Region between the 2 radii and on arc of the circle
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Segment of circle
Region between chord and arc of circle ; a/360 x pi x r^2 -1/2 bh \= a segment
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Annulus
Region between 2 congruent circles
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Prism surface area conjecture
ap+(bh)n
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SA of cylinder
2( pi x r^2) + ( 2 x pi x r ) h
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SA of regular pyramid
1/2 p(l+a)
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SA of cone
pi x r (r + l)
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Pythagorean Theorem
IN a right triangle, the sum of the squares of the lengths of the lengths of the legs equal the square of the hypotenuse
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Converse Pythagorean Theorem
If the lengths of the 3 sides of a triangle satisfy the pythagorean equation, then the triple is a right triangle
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Isosceles right triangle conjecture
IN an iscoseles right triangle, if the legs have length 1, then the hypotenuse has length 1 root 2
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30 - 60 - 90 Triangle Conjecture
In a 30-60-90 triangle, if the shorter leg has length a, then the longer leg has a root 3 and the hypotenuse has length 2a
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Distance formula
The distance between points A (x1, y1) and B ( x2, y2) is given by (AB) ^ 2 \= (x2-x1) ^ 2 + ( y2 - y1 ) ^ 2
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Rectangular Prism Volume Conjecture
if B is the area of the base of a right rectangular prism and H is the height of the solid, then the formula for the volume is V\=Bh
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Right prism Cylinder Volume Conjecture
If B is the area of the base of a right prism (cylinder) and H is the height of the solid, then the formula for the volume is V\=bh
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Oblique Prism - Cylinder Conjecture
Value of an oblique prism (or cylinder) is the same as the value of a right prism ( or cylinder ) that has the same base area and the same height
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Prism Cylinder Volume Conjecture
Volume of a prism or a cylinder is the area of the base multiplied by height
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Pyramid cone Volume
if be is the area of the base of a pyramid or a cone and A is the height of the solid, then the formula for the volume is V \= 1/3 bh
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Sphere volume conjecture
The volume of sphere with a radius r is given by the formula V \= 4/3 pi x r^3
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Sphere surface area conjecture
The surface area, S, of a sphere with radius, r, is given by the formula A\=4 x pi x r^2
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Point
A location in space.
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Line
a straight, continuous arrangement of infinitely many points
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Ray
begins at a point and extends infinitely in one direction
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Line Segment
Consists of 2 points called end point of the segment and all points between
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Plane
Has length and width but no thickness
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Collinear points
points on the same line
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Coplanar points
Points on the same plane
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Angle
2rays that have a common angle
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endpoint
When a ray or line segment begins also where a line segment ends
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midpoint
point on a segment that is the same distance from both endpoints
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Adjacent Angles
2 angles that are next to each other & share a common side
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Vertical Angles
2 angles across from each other on intersecting lines
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Linear Pair
2 angles that are adjacent and supplementary
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supplementary angles
2 angles whose sum is 180 degrees
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Complementary Angles
any 2 angles whose sum is 90 degrees
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Angle Bisector Conjecture
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
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Triangle Sum Conjecture
The sum of the measures of the triangles in every triangle is 180 degrees
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Isosceles Triangle Conjecture
If a triangle is isosceles, then its base angles are congruent
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Triangle inequality conjecture
Sum of the lengths of any 2 sides of a triangle is greater than the length of the third side
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Triangle Exterior Angle Conjecture
Measure of exterior angle is \= to the sum of the measures of the interior angles
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SSS conjecture
If 3 sides of a triangle are congruent to the 3 sides of another triangle, then the triangles are congruent
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SAS Conjecture
if 2 sides and included angle of one triangle is congruent to 2 sides and included angle of another triangle, then triangles are congruent.
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ASA conjecture
2 angles and included angle of 1 triangle are congruent to two angles and included side of another triangle, then triangles are congruent
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Vertex angle bisector conjecture
In an isosceles triangle,the bisector of the vertex angle is the altitude, the median to the base.
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Equilateral / equiangular conjecture
Every equilateral triangle is equiangular. Conversely, every equiangular triangle is equilateral.
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Polygon Sum conjecture
sum of the measures of the interior angles of an n-gon is 180(n-2)
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Quadrilateral Sum conjecture
Sum of the measures of the interior angles of any quadrilateral is 360 degrees
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Pentagon Sum Conjecture
the sum of the measure of any pentagon is 540 degrees
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Exterior angle conjecture
for any polygon, sum of the measures of exterior angles is 360
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Equiangular polygon conjecture
You can find the measure of each interior angle of an equiangular n-gon by either using 180 - 360/n or 180 (n-2)/n
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Kite angle Conjecture
the non vertex angle are congruent
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Kite diagonals conjecture
The diagonals of a kite are perpendicular
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Kite diagonal bisector conjecture
The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal
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Kite angle bisector
The vertex angles of a kite are bisected by a diagonal
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Isosceles trapezoid conjecture
The base angles of an isosceles trapezoid are congruent
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Isosceles trapezoid diagonal conjecture
the diagonal of an isosceles trapezoid are congruent
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Trapezoid consecutive angles conjecture
the consecutive angles between the bases of a trapezoid are supplementary
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3 mid segment conjecture
the 3 mid segments of a cone divided by 4 congruent triangles
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Triangle midsegment conjecture
A midsegment og a triangle is parallel to the 3rd side and the 1/2 length
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Trapezoid midsegment conjecture
the midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the lengths of the bases
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Parallelogram opposite angles conjecture
The opposite angles of a parallelogram are congruent
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Rectangle Consecutive angle conjecture
the consecutive angles of parallelogram are supplementary
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Parallelogram opposite sides conjecture
opposite sides of a parallelogram are congruent
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Double edged straightedge conjecture
if 2 parallel lines are intersected by a 2nd pair of parallel lines that are the same distance apart as the 1st pair, then the parallelogram formed is a rhombus
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rhombus diagonal conjecture
the diagonals of a rhombus are perpendicular and they bisect each other
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rhombus angles conjecture
the diagonals of a rhombus bisect the angles of the rhombus
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Rectangle diagonal conjecture
Diagonals of a rectangle are congruent and bisect each other
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square diagonal conjecture
the diagonals of a square are congruent, perpendicular, and bisect each other