Final Exam Conjecture

Conjectures

Tangent Conjecture

Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to the point of tangency

Chord Arcs Conjecture

2 chords in a circle are congruent then their intercepted arcs are congruent

Chord Central Angles Conjecture

if 2 chords in a circle are congruent then they determine 2 central angles that are congruent

Perpendicular chord conjecture

The perpendicular from the center of a circle to the chord is the bisector of the chord

Perpendicular Bisector of a chord conjecture

The perpendicular bisector of a chord passes through the center of a circle (diameter)

Chord distance to center conjecture

2 congruent chords in a circle are equidistant from the center of the circle

Inscribed Angle Conjecture

measure of an angle inscribed in the circle is the measure of the intercepted arc

Inscribed angles intercepting arcs conjecture

Inscribed angles that intercept the same arc are congruent

Cyclic Quadrilateral Conjecture

The opposite angles of a cyclic quadrilateral are supplementary

Parallel lines intercepted arcs conjecture

Parallel lines intercept congruent arcs on a circle

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

Arc length conjecture

the length go an arc = the measure of the arc divided by 360 degrees times the circumference

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

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

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

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

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

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

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.

Sector of a circle

Region between the 2 radii and on arc of the circle

Segment of circle

Region between chord and arc of circle ; a/360 x pi x r^2 -1/2 bh = a segment

Annulus

Region between 2 congruent circles

Prism surface area conjecture

ap+(bh)n

SA of cylinder

2( pi x r^2) + ( 2 x pi x r ) h

SA of regular pyramid

1/2 p(l+a)

SA of cone

pi x r (r + l)

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

Converse Pythagorean Theorem

If the lengths of the 3 sides of a triangle satisfy the pythagorean equation, then the triple is a right triangle

Isosceles right triangle conjecture

IN an iscoseles right triangle, if the legs have length 1, then the hypotenuse has length 1 root 2

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

Distance formula

The distance between points A (x1, y1) and B ( x2, y2) is given by (AB) ^ 2 = (x2-x1) ^ 2 + ( y2 - y1 ) ^ 2

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

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

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

Prism Cylinder Volume Conjecture

Volume of a prism or a cylinder is the area of the base multiplied by height

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

Sphere volume conjecture

The volume of sphere with a radius r is given by the formula V = 4/3 pi x r^3

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

Point

A location in space.

Line

a straight, continuous arrangement of infinitely many points

Ray

begins at a point and extends infinitely in one direction

Line Segment

Consists of 2 points called end point of the segment and all points between

Plane

Has length and width but no thickness

Collinear points

points on the same line

Coplanar points

Points on the same plane

Angle

2rays that have a common angle

endpoint

When a ray or line segment begins also where a line segment ends

midpoint

point on a segment that is the same distance from both endpoints

Adjacent Angles

2 angles that are next to each other & share a common side

Vertical Angles

2 angles across from each other on intersecting lines

Linear Pair

2 angles that are adjacent and supplementary

supplementary angles

2 angles whose sum is 180 degrees

Complementary Angles

any 2 angles whose sum is 90 degrees

Angle Bisector Conjecture

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

Triangle Sum Conjecture

The sum of the measures of the triangles in every triangle is 180 degrees

Isosceles Triangle Conjecture

If a triangle is isosceles, then its base angles are congruent

Triangle inequality conjecture

Sum of the lengths of any 2 sides of a triangle is greater than the length of the third side

Triangle Exterior Angle Conjecture

Measure of exterior angle is = to the sum of the measures of the interior angles

SSS conjecture

If 3 sides of a triangle are congruent to the 3 sides of another triangle, then the triangles are congruent

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.

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

Vertex angle bisector conjecture

In an isosceles triangle,the bisector of the vertex angle is the altitude, the median to the base.

Equilateral / equiangular conjecture

Every equilateral triangle is equiangular. Conversely, every equiangular triangle is equilateral.

Polygon Sum conjecture

sum of the measures of the interior angles of an n-gon is 180(n-2)

Quadrilateral Sum conjecture

Sum of the measures of the interior angles of any quadrilateral is 360 degrees

Pentagon Sum Conjecture

the sum of the measure of any pentagon is 540 degrees

Exterior angle conjecture

for any polygon, sum of the measures of exterior angles is 360

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

Kite angle Conjecture

the non vertex angle are congruent

Kite diagonals conjecture

The diagonals of a kite are perpendicular

Kite diagonal bisector conjecture

The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal

Kite angle bisector

The vertex angles of a kite are bisected by a diagonal

Isosceles trapezoid conjecture

The base angles of an isosceles trapezoid are congruent

Isosceles trapezoid diagonal conjecture

the diagonal of an isosceles trapezoid are congruent

Trapezoid consecutive angles conjecture

the consecutive angles between the bases of a trapezoid are supplementary

3 mid segment conjecture

the 3 mid segments of a cone divided by 4 congruent triangles

Triangle midsegment conjecture

A midsegment og a triangle is parallel to the 3rd side and the 1/2 length

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

Parallelogram opposite angles conjecture

The opposite angles of a parallelogram are congruent

Rectangle Consecutive angle conjecture

the consecutive angles of parallelogram are supplementary

Parallelogram opposite sides conjecture

opposite sides of a parallelogram are congruent

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

rhombus diagonal conjecture

the diagonals of a rhombus are perpendicular and they bisect each other

rhombus angles conjecture

the diagonals of a rhombus bisect the angles of the rhombus

Rectangle diagonal conjecture

Diagonals of a rectangle are congruent and bisect each other

square diagonal conjecture

the diagonals of a square are congruent, perpendicular, and bisect each other