Term
|
Definition
| Coplanar lines that do not intersect |
|
|
Term
|
Definition
| Noncoplanar lines, therefore they are neither parallel nor intersecting |
|
|
Term
|
Definition
| a line that intersects two coplanar lines at two distinct points |
|
|
Term
| Alternate Interior Angles |
|
Definition
| 2 nonadjacent interior angles on opposite sides of the transversal |
|
|
Term
| Same-Side Interior Angles |
|
Definition
| two interior angles on the same side of the transversal |
|
|
Term
|
Definition
| two angles in corresponding positions relative to the two lines |
|
|
Term
Theorem
If two parallel planes are cut by a third plane, then |
|
Definition
Theorem
then the lines of intersection are parallel |
|
|
Term
Postulate for proving lines parallel
If two lines are cut by a transversal and corresponding angles are congruent, then |
|
Definition
| then the lines are parallel |
|
|
Term
Theorem
If two lines are cut by a transversal and same side interior (exterior) angles are congruent, then |
|
Definition
Theorem
then the lines are parallel |
|
|
Term
Theroem
If two lines are cut by a transversal and same side interior (exterior) angles are supplementary, then |
|
Definition
Theorem
then the lines are parallel |
|
|
Term
Theorem
In a plane, two lines perpendicular to the same line |
|
Definition
|
|
Term
Theorem
Through a point not on a line, |
|
Definition
Theorem
ther is exactly one line parallel to the given line |
|
|
Term
Theorem
Through a point not on a line, |
|
Definition
Theorem
there is exactly one line perpendicular to the given line |
|
|
Term
Theorem
Two lines parallel to a third line... |
|
Definition
Theorem
are parallel to each other |
|
|
Term
|
Definition
- A figure formed by 3 segments joining three noncollinear points
- vertex (vertices)
- sides
- angles
|
|
|
Term
|
Definition
| a line (or ray or segment) added to a diagram to help with the proof |
|
|
Term
Theorem
The sum of the angles of a triangle |
|
Definition
|
|
Term
|
Definition
| a statement that can easily be proved by a theorem |
|
|
Term
Corollary
If two angles of one triangle are congruent to two angles of another triangle, then |
|
Definition
| then the third angles are congruent |
|
|
Term
Corollary
Each angle of an equiangular triangle |
|
Definition
|
|
Term
Corollary
In a triangle, there can be at most |
|
Definition
| one right or obtuse angle |
|
|
Term
Corollary
The acute angles of a right a triangle |
|
Definition
|
|
Term
Theorem
The measure of an exterior angle of a triangle |
|
Definition
Theorem
equals the sum of the measures of the remote interior angles |
|
|
Term
| a circle is not a polygon |
|
Definition
| beause it is not made of segments |
|
|
Term
|
Definition
| A closed plane figure with at least three sides. The sides intersect only at their endpoints and no adjacent sides are collinear. |
|
|
Term
|
Definition
| a polygon in which no diagonal contains points outside the polygon |
|
|
Term
|
Definition
| a ploygon in which a diagonal contains points outside the polygon |
|
|
Term
|
Definition
a segment that connects two non-consecutive vertices
|
|
|
Term
| how do you find how many diagonals can be drawn from one vertex? |
|
Definition
n-3
n =number of sides in the polygon
(and if diagonals have been drawn from one vertex, then the number of triangles they form multiplied by 180 equals the sum of all interior angles in the polygon) |
|
|
Term
Theorem
The sum of the measures of the angles of a convex polygon with n sides is |
|
Definition
|
|
Term
Theorem
The sum of the measures of the exterior angles of any convex polygon, one at each vertex is |
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
equilateral and equiangular
(all sides and angles are congruent) |
|
|
Term
|
Definition
produces a conclusion based on accepted statements (definitions, postualtes, previos theorems, corollaries, given info)
*conclusions must be true if hypothesis is true |
|
|
Term
|
Definition
produces a conclusion based on several past observations
*conclusion is probably true, but not necessarily |
|
|
