Geometry Semester 2 Vocab

*AA Similarity Theorem

if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar

adjacent arcs

arcs of a circle that have exactly one point in common

altitude of a triangle

the perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side

angle of depression

an angle formed by a horizontal line of sight down to an object

angle of elevation

an angle formed by a horizontal line and a line of sight down to an object

apothem

the distance from the center to any side of a regular polygon

arc length

a portion of the circumference of a circle

central angle of a circle

an angle formed by two radii; an angle whose vertex is the center of a circle

chord

a segment whose endpoints are on a circle

circle

the set of all points in a plane that are equidistant from a given point

circumference

the distance around a circle

circumscribed circle

a circle that contains all the vertices of an inscribed polygon

common tangent

a line or segment of lines that is tangent to two coplanar circles

concentric circles

coplanar circles that have a common center

*cone

a three-dimensional geometric solid that tapers smoothly from a flat base to a single point

congruent arc

arcs that have the same measure and are of the same circle or congruent arcs

congruent circles

circles that can be mapped onto each other by a rigid motion or a composition of rigid motions

cosine ratio

a trigonometric function for an acute angle of a right triangle

cross section

the intersection of a plane and a solid

diagonal

a segment that joins two nonconsecutive vertices of a polygon

edge of a polyhedron

a line formed by the intersection of two faces of a polyhedron

equiangular polygon

a polygon in which all the angles are congruent

equidistant

a point that is the same distance from two figures

equilateral polygon

a polygon in which all sides are congruent

external segment

the part of a secant segment that is outside the circle

face of a polygon

a flat surface of a polyhedron

geometric mean

the positive number that satisfies a/x=x/b

inscribed angle

an angle whose vertex is on a circle and whose sides contain chords of a circle

inscribed polygon

a polygon in which all the vertices lie on a circle

intercepted arc

an arc that lies between two lines, rays, or segments

isosceles trapezoid

a trapezoid with congruent legs

kite

a quadrilateral that has two pairs of consecutive, congruent sides, but opposite sides are not congruent

law of cosines

for triangle ABC with side lengths of a, b, and c

a² = b² + c² - 2bc cosA

b² = c² + a² - 2ac cosB

c² = a² + b² - 2ab cosC

law of sines

for triangle ABC with side lengths of a, b, and c

sinA/a = sinB/b = sinC/c and a/sinA= b/sinB = c/sinC

major arc

an arc with a measure greater than 180 degrees

median of a triangle

a segment from a vertex of a triangle to the midpoint of the opposite side

midsegment of a trapezoid

the segment that connects the midpoints of the legs of a trapezoid

midsegment of a triangle

a segment that connects the midpoints of two sides of a triangle

minor arc

an arc with a measure less than 180 degrees

parallelogram

a quadrilateral with both pairs of its opposite sides parallel

perpendicular bisector

a line that is perpendicular to a segment at its midpoint

point of tangency

the point at which a tangent line intersects a circle

polyhedron

a solid that is bounded by a polygon

*prism

a solid that has two faces that are parallel and congruent

*Pythagorean inequalities

mathematical relationships between the sides on a non-right triangle:

a² + b² = c² - right triangle

a² + b² > c² - acute triangle

a² + b² < c²- obtuse triangle

*Pythagorean theorem

states that for all right triangles the square of the hypotenue is equal to the sum of the squares of the legs a² + b² = c²

Pythagorean triple

a set of 3 positive integers to satisfy a² + b² = c²

radian

a unit of measurement for angles

radius of a circle

a segment whose endpoints are the center and any point on a circle

rectangle

a parallelogram with four right angles

regular polygon

a convex polygon that is both equilateral and equiangular

rhombus

a parallelogram with four congruent sides

*SAS Similarity Theorem

if two sides of one triangle are proportional to two sides of another triangle and their included angles then the two triangles are similar

secant of a circle

a line that intersects a circle in two points

sector of a circle

the region bounded by two radii of the circle and their intercepted arc

segments of the chord

the segments formed from two chords that intersect in the interior of a circle

semicircle

an arc with endpoints that are the endpoints of a diameter

sine ratio

for an acute angle of a right triangle, the ratio of the length of the leg opposite the acute angle to the length of the hypotenuse

solve a right triangle

to find all unknown side length and angle measures of a right triangle

*sphere

a three dimensional round-shaped object with no vertices or edges

square

a parallelogram with four congruent sides and four right angles

*SSS Similarity Theorem

if the corresponding sides of a triangle are proportional, then the triangles are similar

standard equation of a circle

(x-h)² + (y-k)² = r² where r is the radius and (h,k) is the center

tangent circles

coplanar circles that intersect in one point

tangent of a circle

a line in the plane of a circle that intersects the circle at exactly one point

tangent

for an acute angle of a right triangle, the ration of the length of the leg opposite the acute angle to the length of the leg adjacent to the acute angle

trapezoid

a quadrilateral with exactly one pair of parallel sides

trigonometric ratio

a ratio of the lengths of two sides in a right triangle

vertex of a polyhedron

a point of a polyhedron where three or more edges meet

volume

the number of cubic units contained in the interior of a solid