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Postulates
Postulate 3-1
30
Mathematics
10th Grade
10/17/2010

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Term
3-1 Corresponding Angles Postulate
Definition

If a transversal intersects 2 parallel lines, then corresponding angles are congruent 

 

 

Term
Theorem 3-1 Alternate Interior Angles
Definition
If a transversal intersects 2 parallel lines, then alternate interior angles are congruent
Term
Theorem 3-2 Same-side Interior Angles
Definition
If a transversal intersects 2 parallel lines, then same side interior angles are supplementary
m<1 + m<2 = 180
Term
Transversal Line
Definition
is a line that intersects 2 lines a differnt planes (coplaner) at 2 points.
Term
Postulates
Definition
statements that are assumed to be true without proof. Postulates serve two purposes - to explain undefined terms, and to serve as a starting point for proving other statements.
Term
Theorums
Definition
are statements that can be deduced and proved from definitions, postulates, and previously proved theorums.
Term
Corresponding angles
Definition
any pair of angles in similar locations with respect to a transversal
Term
Vertical Angle
Definition
the angle formed by the equilateral (equal in length) sides of an isoscoles triangle
Term
Isosceles triangle
Definition
a triangle with two sides of equal length
Term
3-3 Alternate Exterior Theorem
Definition
If a transversal intersects 2 parallel lines, then alternate exterior angles are congruent
Term
3-4 Same Side Exterior Angles
Definition
If a transversal intersects 2 parallel lines, the same-side exterior angles are supplementary
m<2 + m<3 = 180
Term
Postulate 3-2- Converse of Corresponding Angles Postulate
Definition
if two lines and a transversal line form corresponding angles which are congruent, then the two lines are parralle
Term
Theoreom 3-5 Converse of Alternate Interior Angles Theorem
Definition
if two lines and a transversal line form alternate interior angles which are congruent, then the two lines are parralle
Term
Theoreom 3-6 Converse of Same Side Interior Angles Theorem
Definition
if two lines and a transversal line form same-side interior angles which are congruent, then the two lines are parralle
Term
Flow Proof
Definition
Arrrows show the logical connections between the statements. The reasons are written below the statements
Term
Theoreom 3-7 Converse of Alternate Exterior Angles Theorem
Definition
if two lines and a transversal line form alternate exterior angles which are congruent, then the two lines are parralle
Term
Theoreom 3-8 Converse of Same Side Exterior Angles Theorem
Definition
if two lines and a transversal line form same-side exterior angles which are congruent, then the two lines are parralle
Term
Theorem 3-9
Definition
If 2 lines are parrallel to the same line, then they are parallel to each other
Term
Theorem 3-10
Definition
In a plane, if two lines are perpendicular to the same line, then they are parrallel
Term
Theorem 3-11
Definition
If a line is perpendicular to one of two parrallel lines, then it is also perpendicular to the other line
Term
Theorem 3-12 Triangle Angle-Sum Theorem
Definition
The sum of the measures of the angles of a triangle is 180
Term
Theorem 3-13 Triangle Exterior Angle Theorem
Definition
The measure of each exterior angle of a triangle equals the sume of the measures of its two remote interior angles
Term
Ploygon
Definition
is a closed plan figure with at least 3 sides that are segements
Term
Convex Polygon
Definition
has no diagonal with points outside the polygon
Term
Concave Polygan
Definition
Has at least one diagonal with points outside the polygan
Term
Theorem 3-14 Polygon Angel-Sum Theorem
Definition
The sum of the measures of the angles of an n-gon is (n-2)180.
Term
Theorem 3-15 Polygon Exterior Angle-Sum Theorem
Definition
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
Term
Equilateral Polygon
Definition
all side congruent
Term
Equiangular Polygon
Definition
has all angles congruent
Term
Regular Polygon
Definition
both equilateral and equianglar
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