Test 2 Flashcards

1
Q

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

A

predicate

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2
Q

statement with a variable

A

open statement

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3
Q

a statement either true or false; sometimes called a proposition

A

closed statement

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4
Q

a way to close an open statement, choosing variable conditions

A

quantification

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5
Q

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

A

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6
Q

“in”

A

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7
Q

a universal quantifier; “all” or “every”

A

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8
Q

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

A

~(∀x)P(x)≡(∃x)~P(x)

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9
Q

~(∃x)P(x)≡(∀x)~P(x)

A

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

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10
Q

Chain of implications leading directly from hypothesis to conclusion

A

direct proof

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11
Q

rule of logic that moves a proof forward ina directly way

A

syllogism

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12
Q

disproof of a conjecture

A

counterexample

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13
Q

(points) lying in the same straight line

A

collinearity

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14
Q

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

A

altitude

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15
Q

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

A

orthocenter

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16
Q

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

A

median

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17
Q

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

A

centroid

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18
Q

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

A

cevian

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19
Q

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

A

circumcircle

20
Q

the point where all 3 perpendicular bisectors of a triangle intersect

A

circumcenter

21
Q

the point at which the angle bisectors of a triangle intersect

22
Q

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

23
Q

the fixed point, O, in a circle

24
Q

the distance, r, in a circle

25
line segment joining two points on a circle
chord
26
line that intersects at exactly one point
tangent
27
the point where a tangent line touched the circle
point of tangency
28
the perimeter of a circle
circumference
29
a piece of the circle
arc
30
a pie-shaped portion of the interior of the circle, bounded by an arc of the circle and two radii
sectors
31
if P, Q, and R are three points on a circle with the center at O, the angle
central angle
32
if P, Q, and R are three points on a circle with center at O, the angle
inscribed angle
33
the center of the incircle, I
incenter
34
a circle interior to the triangle that is tangent to all three sides of the triangle
incircle
35
a circler exterior to the triangle and tangent to one side and to extensions of the other two sides
excircle
36
If two circles' tangents are perpendicular at their points of intersection
orthogonal
37
the region bounded by the three semicircular arcs on one side of the diameter AB of a circle
arbelos
38
another "father" of geometry, authored Foundations of Geometry, also known for defining Hilbert's space and organizing Euclid's axioms into five groups
David Hilbert
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"
axiom of incedence
40
how we know when a point is between two other points, or a ray is between two other rays
axiom of betweeness
41
tools for developing proofs, used to apply theorems to particular situations
modus ponens
42
tool for developing proofs, prove the contrapositive of the conjecture (indirect proof)
modus tollens
43
preliminary result needed to prove a particular theorem
lemma
44
a result follows fairly easily from a previous result
corollary
45
power of P with respect to C, d^2-r^2
Power (P,C)
46
line formed from the set of points P for which the power is the same value from both circles
Radical Axis
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.
axiom of congruence