integrated geometry terms from second semester
½ap = ½ apothem*perimeter
Theorems:
6.1: opposite sides of parallelograms are congruent
6.2: opposite angles of a parallelogram are congruent
6.3: diagonals of a parallelogram bisect eachother
6.9: each diagonal of a rhombus bisects two angles of the rhombus
6.10: the diagonals of a rhombus are perpendicular
6.11:the diagonals of a rectangle are congruent
6.15: the base angles of an isos. trap. are congruent
6.16: the diagonals of an isos. trap. are…

Parallelogram
a quadrilateral with both pairs of opposite sides parallel

Rhombus
a parallelogram with four congruent sides

Rectangle
a parallelogram with four right angles

Square
a parallelogram with four congruent sides and four right angles

Kite
a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

trapezoid
a quadrilateral with exactly one pair of parallel sides

isoscles trapezoid
a trapezoid whose nonparallel sides are congruent

consecutive angles
angles of a polygon that share a side

base angles of a trapezoid
two angles that share a base of a trapezoid (congruent in isos. trap.)

midsegment of a trapezoid
the segment that joins the midpoints of the nonparallel opposite sides of a trapezoid

trapezoid midsegment theorem
1) the midsegment of a trapezoid is parallel to the bases 2) the length of the midsegment of a trapezoid is the average of the bases

base of a parallelogram
any side of the parallelogram

altitude
a segment perpendicular to the line containing that base drawn from the side opposite the base

height
length of altitude

area of a rectangle or parallelogram
b*h

area of a triangle
½(b*h)

pythagorean theorem
the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse

pythagorean triple
a set of nonzero whole numbers a, b, and c that satisfy the pythagorean theorem

45-45-90 triangle theorem
hypotenuse = √2*leg

30-60-90 triangle theorem
hypotenuse = 2short leg; long leg = √3 short leg

height of a trapezoid
the perpendicular distance between the bases

area of a trapezoid
½h(b1*b2)

are of a rhombus or kite
½d1*d2

radius of regular polygon
distance from the center to any given vertex

apothem
perpendicular distance from the center to any given side

area of a regular polygon
½ap

circle
set of points all equidistant from a given point called center

radius
segment with one endpoint on circle and other on center

congruent circles
have congruent radii

diameter
segment with both endpoints on circle passing through center

central angle
an angle whose vertex is the center of the circle

minor arc
an arc smaller than a semicircle

major arc
an arc larger than a semicircle

adjacent arcs
arcs of the same circle that have exactly one point in common

arc addition postulate
mABC=mAB+mBC

circumference
distance around a circle; πd or 2πr

pi (π)
ratio of the circumference of a circle to it's diameter

concentric circles
circles on same plane with same centers

arc length theorem
length of AB = mAB/360*2πr

congruent arcs
arcs that have the same measure and are in the same circle or in congruent circles

sector of a circle
region bound by an arc of the circle and the two radii to the arc's endpoints

segment of a circle
region bound by an arc and the segment joining its endpoints

area of a sector of a circle
area of sector AOB = mAB/360*πr²

proportion
a statement that two ratios are equal; a/b = c/d; a:b = c:d

extended proportion
a statement that three or more ratios are equal; a/b = c/d = e/f; a:b = c:d = e:f

cross-product property
multiplying both sides of a/b = c/d by bd

similar (~)
two figures that have the same shape but no necessarily the same size

similarity ratio
the ratio of lengths of corresponding sides