Geometry Test 2

Front 1

bi-right

Back 1

quadrilateral ABDC in which the adjacent angles A and B are right angles (denoted so that the first 2 letters denote vertices at which the quadrilateral has right angles)

Front 2

Saccheri Quadrilateral

Back 2

an isoscles bi-right quadrilateral: quadrilateral ABDC is one whose sides are congruent

Front 3

Lambert quadrilateral

Back 3

a quadrilateral with at least three right angles, but not assuming anything about the 4th angle1

Front 4

Semi-Euclidean

Back 4

a Hilbert plane is called semi-Euclidean if all Lambert quad. and all Saccheri quad. are rectangles

Front 5

acute angle hypothesis

Back 5

if the fourth angle of every Lambert quad. is acute, then the plane satisfies the acute angle hypothesis

Front 6

obtuse angle hypothesis

Back 6

if the fourth angle of every Lambert quad. is obtuse then the plane satisfies the obtuse angle hypothesis

Front 7

exterior angle theorem

Back 7

in any Hilbert plane, an exterior angle of a triangle is greater than either remote interior angle

Front 8

remote interior angles

Back 8

the two angles of a triangle that are not supplementary to the exterior angles

Front 9

exterior angle

Back 9

an angle supplementary to an angle of a triangle

Front 10

Alternate Interior Angle theorem

Back 10

in any Hilbert plane, if two lines cut by a transversal have a pair of congruent alternate interior angles with respect to the transversal, then the two lines are parallel

Front 11

AIA Corollary 1

Back 11

two lines perpendicular dropped from line are parallel. Hence the perpendicular dropped from a point P not on line l to l is unique

Front 12

AIA corollary 2

Back 12

if l is any line and P is any point not on l, there exists at least one line m through P parallel to l (standard configuration)

Front 13

EA corollary 1

Back 13

if a triangle has a right or obtuse angle, the other two angles are acute

Front 14

converse of AIA

Back 14

if two lines are parallel, then alternate interior angles cut by a transversal are congruent

Front 15

Euclid's 5th postulate <->

Back 15

Hilbert's Euclidean parallel postulate

Front 16

Aristotle's axiom

Back 16

given any side of an acute angle and any segment AB, there exists a point Y on the given side of the angle such that if X is the foot of the perpendicular from Y to the other side, XY>AB

Front 17

Non-obtuse angle theorem

Back 17

a Hilbert plane satisfying Aristotle's axiom either is semi-Euclidean or satisfies the acute angle hypothesis (so that by Saccheri's angle theorem, the angle sum of every triangle is <=180 degrees

Front 18

Spherical geometry

Back 18

In spherical geometry, incidence axiom 1 fails. In spherical and elliptic geometries, betweenness axiom fails.

Front 19

HEPP<->

Back 19

if a line intersects one of two parallel lines, then it also intersects the other

Front 20

HEPP<->

Back 20

converse to the alternate interior angle theorem

Front 21

HEPP<->

Back 21

if t is a transversal to l and m, l is parallel to m, and t is parallel to l, then t is perpendicular to m

Front 22

HEPP<->

Back 22

if k is parallel to l, m is perpendicular to k, and n is perpendicular to l, then either m=n or m is parallel to n