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53 terms

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

a²+b²=c²

right triangle

a²+b²>c²

acute triangle

a²+b²<c²

obtuse triangle

45-45-90 triangle theorem

hypotenuse = √2*leg

30-60-90 triangle theorem

hypotenuse = 2**short leg; long leg = √3**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

semicircle

half a 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 circle

πr²

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