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Theorems
Theorems 1-58
58
Mathematics
8th Grade
12/12/2011
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Term
Theorem 1
 Definition
If two angles are right angles, then they are congruent.
Term
Theorem 2
 Definition
If two angles are straight angles, then they are congruent.
Term
Theorem 3
 Definition
If a conditional statement is true, then the contrapositive of the statement is also true. (If p, then q <-> If ~q, then ~p.)
Term
Theorem 4
 Definition
If angles are supplementary to the same angle, then they are congruent.
Term
Theorem 5
 Definition
If angles are supplementary to congruent angles, then they are congruent.
Term
Theorem 6
 Definition
If angles are complementary to the same angle, then they are congruent.
Term
Theorem 7
 Definition
If angles are complementary to congruent angles, then they are congruent.
Term
Theorem 8
 Definition
If a segment is added to two congruent segments, the sums are congruent. (Addition Property)
Term
Theorem 9
 Definition
If an angle is added to two congruent angles, the sums are congruent. (Addition Property)
Term
Theorem 10
 Definition
If congruent segments are added to congruent segments, the sums are congruent. (Addition Property)
Term
Theorem 11
 Definition
If congruent angles are added to congruent angles, the sums are congruent. (Addition Property)
Term
Theorem 12
 Definition
If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property)
Term
Theorem 13
 Definition
If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property)
Term
Theorem 14
 Definition
If segments (or angles) are congruent, their like multiples are congruent. (Mulitplication Property)
Term
Theorem 15
 Definition
If segments (or angles) are congruent, their like divisions are congruent. (Division Property)
Term
Theorem 16
 Definition
If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (Transitive Property)
Term
Theorem 17
 Definition
If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. (Transitive Property)
Term
Theorem 18
 Definition
Vertical angles are congruent.
Term
Theorem 19
 Definition
All radii of a circle are congruent.
Term
Theorem 20
 Definition
If two sides of a triangle are congruent, the angles opposite the sides are congruent.
Term
Theorem 21
 Definition
If two angles of a triangle are congruent, the sides opposite the angles are congruent.
Term
Theorem 22
 Definition
If A=(x1,y1) and B=(x2,y2), the the midpoint of AB can be found using the midpoint formula.
Term
Theorem 23
 Definition
If two angles are both supplementary and congruent, then they are right angles.
Term
Theorem 24
 Definition
If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment.
Term
Theorem 25
 Definition
If a points is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment.
Term
Theorem 26
 Definition
If two nonvertical lines are parallel, then their slopes are equal.
Term
Theorem 27
 Definition
If the slopes of two nonvertical lines are equal, then the lines are parallel.
Term
Theorem 28
 Definition
If two lines are perpendicularand neither is vertical, each line's slope is the opposite reciprocal of the others.
Term
Theorem 29
 Definition
If a line's slope is the opposite reciprocal of the others, the two lines are perpendicular.
Term
Theorem 30
 Definition
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.
Term
Theorem 31
 Definition
If two lines are cut by a transversal such that two alternate interior angles are congruent, the lines are parallel.
Term
Theorem 32
 Definition
If two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel.
Term
Theorem 33
 Definition
If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel.
Term
Theorem 34
 Definition
If two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, the lines are parallel.
Term
Theorem 35
 Definition
If two lines are cut by a transversal such that two exterior angles on the same side of the transversal are supplementary, the lines are parallel.
Term
Theorem 36
 Definition
If two coplanar lines are perpendicular to a third line, they are parallel.
Term
Theorem 37
 Definition
If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent.
Term
Theorem 38
 Definition
If two parallel lines are cut by a transversal, then any pair of the angles formed are either congruent or supplementary.
Term
Theorem 39
 Definition
If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent.
Term
Theorem 40
 Definition
If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent.
Term
Theorem 41
 Definition
If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.
Term
Theorem 42
 Definition
If two parallel lines are cut by a transversal, each pair of exterior angles on the same side of the transversal are supplementary.
Term
Theorem 43
 Definition
In a plane, if a line is perpendicular to one of two parallel lines, is is perpendicular to the other.
Term
Theorem 44
 Definition
If two lines are parallel to a third line, they are parallel to each other. (Transitive Property or Parallel Lines)
Term
Theorem 45
 Definition
A line and a point not on the line determine a plane.
Term
Theorem 46
 Definition
Two intersecting lines determine a plane.
Term
Theorem 47
 Definition
Two parallel lines determine a plane.
Term
Theorem 48
 Definition
If a line is perpendicular to two distinct lines that lie in a plane and pass through its foot, then it is perpendicular to the plane.
Term
Theorem 49
 Definition
If a plane intersects two parallel planes, the lines of intersection are parallel.
Term
Theorem 50
 Definition
The sum of the measures of the three angles of a triangle is 180.
Term
Theorem 51
 Definition
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Term
Theorem 52
 Definition
A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side. (Midline Theorem)
Term
Theorem 53
 Definition
If two angles of a triangle are congruent to two angles of a second triangle, then the third angles are congruent. (No-Choice Theorem)
Term
Theorem 54
 Definition
If there exists a correspondance between the vertices of two triangles such that two angles and a nonincluded side of one are congruent to the corresponding parts of the other, then the triangles are congruent. (AAS)
Term
Theorem 55
 Definition
The sum of the measures of the angles of a polygon with n sides is given by the formula: (n-2)180.
Term
Theorem 56
 Definition
If one exterior angle is taken at each vertex, the sum of the measures of the exterior angles of a polygon equals 360.
Term
Theorem 57
 Definition
The number of the diagonals that can be drawn in a polygon of n sides is given by the formula: n(n-3)/2
Term
Theorem 58
 Definition
The measure of each exterior angle of an equiangular polygon of n sides is given by the formula 360/n.
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