Geometry Theorems X>14

Front 1

the intersection of a sphere with a plane through its center is a circle with the _____ center and ____ radius

Back 1

same

Front 2

A line perpendicular to a radius at its outer end is a

Back 2

tangent to a circle

Front 3

Every tangent is ___ to a radius drawn to the point of contact

Back 3

perpendicular

Front 4

the perpendicular from the center of a circle ___ the chord

Back 4

bisects the chord

Front 5

the segment from the center of a circle to the midpoint of a circle (not diameter)

Back 5

is perpendicular to the chord

Front 6

in the lane of a circle, the perpendicular bisector of a chord

Back 6

passes through the center

Front 7

In the same circle or in conguent circles, any two congruent chords

Back 7

are equidistant from the center.

Front 8

the line-circle theorem

Back 8

if a line and a circle are coplanar and the line intersects the circle, the intersection of the circle is two and only two points

Front 9

a plane perpendiuclar to a radius at its outer end is

Back 9

tangent to the sphere

Front 10

Every tangent plane to a sphere is

Back 10

perpendicular to the radius drawn to the point of contact.

Front 11

If a plane intersects the interior of a sphere, the intersection of the palen and the sphere is a

Back 11

circle. The center o this circle is the foot of the perpendicular from the center of the sphere to the plane.

Front 12

the perpendicular from the center of a sphere to a chord

Back 12

bisects the chord.

Front 13

the segment from the center of a sophere to a chord

Back 13

bisects the chord

Front 14

the segment from the center of a sphere to a midpoint of a chord

Back 14

is perpendicular to the chord

Front 15

The arc addition theorem

Back 15

you can add arcs

Front 16

inscribed angle theorem

Back 16

measure of inscribed angle is half the intercepted arc

Front 17

in same or congruent circles, if two chords are congruent then so are the

Back 17

corresponding minor arcs

Front 18

if two arcs are congruent then so are the

Back 18

corresponding chords

Front 19

tangent-secant theorem

Back 19

given an angle with its vertex on a circle formed by the secant ray and a tangent ray. The measure of the angle is half the measure of the intercepted arc

Front 20

the two tangent theorem

Back 20

the two tangent segments to a circle from a point of the exterior are congruent and determine congruent angels with the segment from the exterior point to the center.

Front 21

The two-secant power theorem

Back 21

outside segment x whole= outside segment x whole *given two secants intersection a circle*

Front 22

the tangent-secant power theorem

Back 22

the segment outside, x the whole= tangent segment^2

Front 23

the two-chord power theorem

Back 23

let there be two chords, the two segments multiplied= the two segments of the other chord. Unlike rest, no need the "whole segment" anymore.

Front 24

angles inscribed in semicircles are

Back 24

always right

Front 25

if two arcs have equal radii

Back 25

their lengths are proportional to their measures

Front 26

the area of a sector (whilst knowing the length) is

Back 26

A=1/2rL

area is half the product of the radius and length of arc.

Front 27

given an apothem and the perimeter of the polyon

Back 27

the area is 1/2 product of perimeter and apothem.

Front 28

the measure of an angle in a polygon is

Back 28

180- 360/n (n being the # of sides, that is)

Front 29

the measure of an exterior angle of a polygon is

Back 29

360/n.

if 180-360/n holds, to find the exterior, you'd say

180-360/n=180-n (because "n" would be the interior) and obviously it cancels out.

Front 30

given two chords, the measure of an angle formed by the chord is

Back 30

1/2 the sum of the two intercepted arcs

Front 31

given two lines that forms an angle in the exterior of the circle, the angle of that is

Back 31

1/2 the difference of the two arcs it intercepts.

Front 32

convex.

Back 32

if you take any two points and connect it, and the line lies in the interior of the polygon it is convex, if not, it's concave.

Front 33

regular polygon:

Back 33

it is regular if it is convex, all the sides are congruent and all angles are congruent.

Front 34

apothem

Back 34

distance from the center of a regular polygon to each of the sides is called the apothem of the polygon.

Front 35

circular region

Back 35

is the union of a circle and its interior

Front 36

inscribed

Back 36

when the vertices of the polygon lies on the circle

Front 37

circumsribed

Back 37

when the polygon is tangent to the circle

Front 38

the ratio of the area of two similar polygons (triangle)is the

Back 38

ratio of their sides, squared.