Math - Important Vocab

Parallel postulate

Given a line m and a point A that is not on line m, there is exactly one line passing through A that is parallel to m

CPCFC

Corresponding parts of congruent figures are congruent

Rhombus

A quadrilateral with 4 congruent sides

Parallelogram property

If a quadrilateral has one pair of opposite sides both parallel and congruent, then it is a parallelogram

Parallel side splitter

If a line divides two sides of a triangle proportionally, the line must be parallel to the third side of the triangle

Perimeter of n-sided polygon

P=n*tan(180/n)

Area of n-sided polygon

A=n*sin(180/n)cos(180/n)

Equation of a circle

(x-h)²+(y-k)²=r²

Distance formula

D= ((x1-x2)²+(y1-y2)²)^1/2

Median

The line segment connecting 1 vertex of a triangle to the midpoint of the opposite side

Centroid

The point where a triangle’s medians intersect. The centroid splits each median into a 2:1 ratio from the vertex to the midpoint of the opposite side

Arc

The part of a circle lying between two points on the circle

Central angle

An angle formed by two rays whose endpoints are the center of the circle

Chord

A line segment whose endpoints are on the circle

Inscribed angle

An angle formed by 2 chords in a circle that share an endpoint

Inscribed angle theorem

The inscribed angle is ½ the measure of the arc that defines it

Tangent line theorem

A tangent line is always perpendicular to the radius of the circle at the point of tangency

Circumscribed

A polygon is circumscribed by a circle if every vertex of the polygon is on the circle

Cyclic quadrilateral

A quadrilateral whose every vertex lies on the circle. Opposite angles of a cyclic quadrilateral are supplementary

Circumcenter

Where all the perpendicular bisectors of a triangle intersect

Circumcenter theorem

The circumcenter is equidistant to all 3 vertices of the triangle, meaning that it is also the center of the circle that circumscribes the triangle

Incenter

The intersection point of a triangle’s angle bisectors.

Incenter theorem

The incenter is the center of the inscribed circle the triangle

Sector

The area between 2 radii of a circle

Area of sector (degrees)

pi*r²*(theta/360)

Area of sector (radians)

1/2r²*theta

Arc length (degrees)

2pi*r²*(theta/360)

Arc length (radians)

r*theta

Radian (the measurement of the angle defining the ratio of arc length to radius)

theta = l/r radians