Term
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Definition
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Term
| Q is an External point of L if |
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Definition
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Term
| Two lines l and m are parallel |
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Definition
| Two lines l and m are parallel if there is no point P s.t P lies on both l and m. |
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Term
| Points A, B, and C are collinear |
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Definition
| There exists one line l s.t A, B, and C all lie on l |
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Term
A*C*B (C is between A and B)
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Definition
| The point C is between A and B if A, B, and C are collinear and AC + CB = AB |
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Term
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Definition
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Term
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Definition
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Term
| Coordinate function of the point P |
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Definition
| Let l be a line. A one-to-one correspondence f : l -> R s.t. PQ = |f(P) - f(Q)| fo every P and Q on l |
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Term
| M is the Midpoint of A and B |
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Definition
If M is between A and B and AM = MB
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Term
| A set of points S is said to be Convex |
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Definition
| If for every pair of points A and B in S, the entire segment AB is contained in S |
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Term
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Definition
Union of two nonopposite rays AB and AC sharing the same endpoint
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Term
| Let A, B, and C be three points s.t that rays AB and AC are nonoposite. What is the interior of angle BAC |
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Definition
| The interior of BAC is defined to be the intersection of the half planes H(b) [determined by B and AC] and the half plane H(c) [detereminded by C and AB] |
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Term
Ray AD is between rays AB and AC
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Definition
| If D is in the interior of BAC |
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Term
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Definition
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Term
| Two angles BAC and EDF are congruent if |
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Definition
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Term
BAC is a:
Right Angle
Acute Angle
Obtuse Angle |
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Definition
BAC = 90
BAC < 90
BAC > 90 |
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Term
| Let A, B, and C be three noncollinear points. A ray AD is an angle bisector of BAC if |
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Definition
| D is in the interior of BAC and BAD = DAC |
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Term
| Two angles BAC and EDF are supplementary if |
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Definition
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Term
| Two angles BAD and DAC for a linear par if |
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Definition
| AB and AC are opposite rays |
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Term
| Two lines l and m are perpendicular if |
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Definition
| There exists a point A that lies on both l and m and there exists a point B on l, and a point C on m s.t. BAC is a right angle |
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Term
| Let D and E be two distinct points. A perpendicular bisector of DE is a |
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Definition
Line n s.t. the midpoint of E lies on n and n perp DE
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Term
| Angles BAC and DAE form a vetical pair if |
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Definition
Rays AB and AE are opposite and AC and AD are opposite OR
if rays AB and AD are opposite and rays AC and AE are opposite |
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Term
| Two triangles are congruent if |
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Definition
corresponding angles are congruent and corresponding sides are congruent
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Term
| A triangle is called isoceles if |
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Definition
| It has a pair of conguent sides |
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Term
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Definition
| The angles not inclued between the congruent sides |
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Term
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Definition
| An angle that forms a linear pair with one of the interior angles |
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Term
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Definition
| If the exteior angle forms a lienar pair with the interior angle at one vertex, then the interior angles at the other two vertices are Remote Interior angles |
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Term
| A triangle is a right traingle if |
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Definition
| One of the interior angles is a right angle |
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Term
| Let l and m be two distinct lines. A thrid line T is called a transversal for l and m if |
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Definition
| t itersects l in one point B and t intersects m in one point C with B not equal to C |
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Term
| Ruler Placement Postulate |
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Definition
For every pair of distinct points P and Q,
there is a coordinate function
f: PQ -> R s.t. f(P) = 0 AND f(Q) > 0 |
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Term
| Betweenness Theorem for Points |
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Definition
Let l be a line, let A,B,C be three distinct points
that all lie on l; and let f: l -> R be a coord function
for l. The point C is between A and B IFF either
f(A) < f(C) < f(B)
OR
f(A) > f(C) > f(B) |
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Term
| Point Construction Postulate |
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Definition
If A and B are distinct points and
d is any nonnegative real number,
then there exists a point C
s.t C lies on AB and AC = d |
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Term
| Existence and Uniqueness of Midpoints |
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Definition
| If A and B are distinct points, then there exists a unique point M s.t. M is the midopint of AB |
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Term
| Betweenness Theorem for Rays |
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Definition
Let A, B, and C, and D be for distinct points s.t
C and D lie on the same side of AB.
Then:
u(LBAD) < u(LBAC) iff
AD is between rays AB and AC
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Term
| Existence & Uniqueness of Angle Bisectors |
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Definition
If A, B, and C are three noncollinear noncollinear points, then there exists a
unique angle bisector for angle BAC |
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Term
| Existence and Uniqueness of Perpendiculars |
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Definition
If D and E are two distinct points,
then there exists a
unique perpendicular bisector for DE |
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Term
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Definition
| Vertical Angles are Congruent |
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Term
| Isoceles Triangle Theorem |
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Definition
| The base angles of an isoceles triangle are congruent |
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Term
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Definition
| The measure of an exterior angle for a triangle is strictly greater than the measure of either remote angle |
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Term
| Angle-Side-Angle Congruence |
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Definition
If 2 angles and the included side of one triangle are congruent to the corresponding parts of a second triangle
then the two triangles are congruent |
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Term
| Converse to the Isoceles Triangle Theorem |
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Definition
| If Triangle ABC is a triangle s.t. angle ABC = angle ACB, then AB = AC |
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Term
| Angle Angle Side Congruence |
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Definition
If ABC and DEF are two triangles s.t.
angle ABC = angle DEF
angle BCA = angle EFD
AC = DF
Then the two triangles are congruent |
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Term
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Definition
| If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and a leg of the second triangle, then the two triangles are congruent |
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Term
| Side-Side-Side Congruence |
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Definition
If Triangles ABC and DEF are 2 triangles s.t
AB =DE
BC = EF
CA = FD
Then the two triangles are congruent |
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Term
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Definition
| In any triangle, the greater side lies opposite the greater angle and the greater angle lies opposite the greater side |
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Term
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Definition
| If A,B,C are noncollinear points, then AC < AB + BC |
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Term
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Definition
If ABC and DEF are two triangles s.t.
AB = DE
AC = DF
u(LBAC) < u(LEDF) then
BC < EF |
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Term
| Pointwise Characterization of Angle Bisector |
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Definition
Let A,B,C be 3 noncollinear points and
let P be a point P be a point in the interior of angle BAC
Then
P lies on the angle bisector of angle BAC iff
d(P, AB) = d(P, AC)
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Term
| Pointwise Characterization of Perpendicular Bisectors |
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Definition
Let A and B be distinct points.
A point B lies on the perp bisector of AB
IFF
PA = PB |
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Term
| Alternate Interior Angles Theorem |
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Definition
If l and l' are two lines cut by a transversial t
in a way that a pair of alternate interior angles are congruent
then l is parallel to l' |
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Term
| Saccheri-Legendre Theorem |
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Definition
If triangle ABC is any triangle, then
o(ABC) </= 180 |
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Term
| Corresponding Angles Theorem |
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Definition
If l and l' are two lines cut by a transverisal in such a way that a pair of alternate interior angles is congruent, then l is parallel to l'
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Term
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Definition
If l is a line and P is an external point, then
there is a line m s.t P lies on m and m is parallel to l |
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