Test 2

Question 1

A statement with a variable, also known as a open statement

Answer 1

predicate

Question 2

statement with a variable

Answer 2

open statement

Question 3

a statement either true or false; sometimes called a proposition

Answer 3

closed statement

Question 4

a way to close an open statement, choosing variable conditions

Answer 4

quantification

Question 5

existential quantifier; “exists” “some” or “at least one”

Answer 5

∃

Question 6

“in”

Answer 6

∈

Question 7

a universal quantifier; “all” or “every”

Answer 7

∀

Question 8

“not” “all x’s” are P(x) = there is at least one x not P(x)

Answer 8

~(∀x)P(x)≡(∃x)~P(x)

Question 9

~(∃x)P(x)≡(∀x)~P(x)

Answer 9

there is not at least one x that are P(x) = all x are no P(x)

Question 10

Chain of implications leading directly from hypothesis to conclusion

Answer 10

direct proof

Question 11

rule of logic that moves a proof forward ina directly way

Answer 11

syllogism

Question 12

disproof of a conjecture

Answer 12

counterexample

Question 13

(points) lying in the same straight line

Answer 13

collinearity

Question 14

the line segment from a vertex perpendicular to the line containing the opposite side

Answer 14

altitude

Question 15

the point at which the three altitudes of a triangle intersect (H)

Answer 15

orthocenter

Question 16

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

Answer 16

median

Question 17

the point where 3 medians of a triangle intersect (G)

Answer 17

centroid

Question 18

segment from vertex of a triangle to a point on the line containing the opposite side

Answer 18

cevian

Question 19

center at the circumcenter and passes through the vertices of the triangle

Answer 19

circumcircle

Question 20

the point where all 3 perpendicular bisectors of a triangle intersect

Answer 20

circumcenter

Question 21

the point at which the angle bisectors of a triangle intersect

Answer 21

incenter

Question 22

the set of points at a fixed distance, r, from a fixed point, O

Answer 22

circle

Question 23

the fixed point, O, in a circle

Answer 23

center

Question 24

the distance, r, in a circle

Answer 24

radius

Question 25

line segment joining two points on a circle

Answer 25

chord

Question 26

line that intersects at exactly one point

Answer 26

tangent

Question 27

the point where a tangent line touched the circle

Answer 27

point of tangency

Question 28

the perimeter of a circle

Answer 28

circumference

Question 29

a piece of the circle

Answer 29

arc

Question 30

a pie-shaped portion of the interior of the circle, bounded by an arc of the circle and two radii

Answer 30

sectors

Question 31

if P, Q, and R are three points on a circle with the center at O, the angle <PQR

Answer 31

central angle

Question 32

if P, Q, and R are three points on a circle with center at O, the angle <PQR

Answer 32

inscribed angle

Question 33

the center of the incircle, I

Answer 33

incenter

Question 34

a circle interior to the triangle that is tangent to all three sides of the triangle

Answer 34

incircle

Question 35

a circler exterior to the triangle and tangent to one side and to extensions of the other two sides

Answer 35

excircle

Question 36

If two circles’ tangents are perpendicular at their points of intersection

Answer 36

orthogonal

Question 37

the region bounded by the three semicircular arcs on one side of the diameter AB of a circle

Answer 37

arbelos

Question 38

another “father” of geometry, authored Foundations of Geometry, also known for defining Hilbert’s space and organizing Euclid’s axioms into five groups

Answer 38

David Hilbert

Question 39

specific exactly what is meant by a point is “on a line,” a line “goes through a point,” or a line “lies in a plane”

Answer 39

axiom of incedence

Question 40

how we know when a point is between two other points, or a ray is between two other rays

Answer 40

axiom of betweeness

Question 41

tools for developing proofs, used to apply theorems to particular situations

Answer 41

modus ponens

Question 42

tool for developing proofs, prove the contrapositive of the conjecture (indirect proof)

Answer 42

modus tollens

Question 43

preliminary result needed to prove a particular theorem

Answer 43

lemma

Question 44

a result follows fairly easily from a previous result

Answer 44

corollary

Question 45

power of P with respect to C, d^2-r^2

Answer 45

Power (P,C)

Question 46

line formed from the set of points P for which the power is the same value from both circles

Answer 46

Radical Axis

Question 47

if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer 47

axiom of congruence