by bubzy


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If two angles are right angles, they are congruent.
Theorem 1
If two angles are straight angles, they are congruent.
Theorem 2
If a conditional statement is true, then the contrapositive of the statement is also true. [If p, then q ↔ If ~q, then ~p.]
Theorem 3
If angles are supplementary to the same angle, then they are congruent. [sup. of the same angle are congruent]
Theorem 4
If angles are supplementary to congruent angles, then they are congruent. [sup. of congruent angles are congruent]
Theorem 5
If angles are complimentary to the same angle, then they are congruent. [comp. of the same angle are congruent]
Theorem 6
If angles are complimentary to congruent angles, then they are congruent. [comp. of congruent angles are congruent]
Theorem 7
If a segment is added to two congruent segments, then their sums are congruent. [Addition Property]
Theorem 8
If an angle is added to two congruent angles, then their sums are congruent. [Addition Property]
Theorem 9
If congruent segments are added to congruent segments, the sums are congruent. [Addition Property]
Theorem 10
If congruent angles are added to congruent angles, the sums are congruent. [Addition Property]
Theorem 11
If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. [Subtraction Property]
Theorem 12
If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. [Subtraction Property]
Theorem13
If segments (or angles) are congruent, their like multiples are congruent. [Multiplication property]
Theorem 14
If segments (or angles) are congruent, their like divisions are congruent. [Division Property]
Theorem 15
If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. [Transitive Property]
Theorem 16
If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. [Transitive Property]
Theorem 17
Vertical Angles are congruent.
Theorem 18
All radii of a circle are congruent.
Theorem 19
If two sides of a triangle are congruent, the angles opposite the sides are congruent.
Theorem 20
If two angles of a triangle are congruent, the sides opposite the angles are congruent.
Theorem 21
If A = (x₁ , y₁) and B = (x₂ , y₂), then the midpoint M = (xm , ym) of AB can be found by using the midpoint formula:
Theorem 22
If two angles are both supplementary and congruent, then they are right angles.
Theorem 23
If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment.
Theorem 24
If a point is on the perpendicular bisector if a segment, then it is equidistant from the endpoints of that segment.
Theorem 25
If two non-vertical lines are parallel, then their slopes are equal.
Theorem 26
If the slopes of two non-vertical lines are equal, then their slopes are equal.
Theorem 27
If two lines are perpendicular and neither is equal, each line’s slope is the opposite reciprocal of the other’s.
Theorem 28
If a line’s slope is the opposite of another line’s slope, the two lines are perpendicular.
Theorem 29
The measure of an exterior angle of a triangle is greater than the measure of any remote interior angle.
Theorem 30
If two lines are cut by a transversal such that the two alternate interior angles are congruent, the lines are parallel. [Alt. int. <’s => || lines.]
Theorem 31
If two lines are cut by a transversal such that the two alternate exterior angles are congruent, the lines are parallel. [Alt. ext. <’s => || lines.]
Theorem 32
If two lines are cut by a transversal such that the two corresponding angles are congruent, the lines are parallel. [Corr. <’s => || lines.]
Theorem 33
If two lines are cut by a transversal such that the two interior angles on the same side of the transversal are supplementary, the lines are parallel.
Theorem 34
If two lines are cut by a transversal such that the two exterior angles on the same side of the transversal are supplementary, the lines are parallel.
Theorem 35
If two coplanar lines are perpendicular to a third line, they are parallel.
Theorem 36
If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent. [|| lines => alt. int. <’s ]
Theorem 37
If two parallel lines are cut by a transversal, then any pair of angles formed are either congruent or supplementary.
Theorem 38
If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent. [|| lines => alt. ext. <’s ]
Theorem 39
If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent. [|| lines => corr. <’s ]
Theorem 40
If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.
Theorem 41
If two parallel lines are cut by a transversal, each pair of exterior angles on the same side of the transversal are supplementary.
Theorem 42
In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other.
Theorem 43
If two lines are parallel to a third line, they are parallel to each other. [Transitive Property of Parallel Lines]
Theorem 44
A line and a point not on the line determine a plane.
Theorem 45
Two intersecting lines determine a plane.
Theorem 46
Two parallel lines determine a plane.
Theorem 47
If a line is perpendicular to two distinct lines that lie in a plane and that pass through its foot, then it is perpendicular to the plane.
Theorem 48
If a plane intersects two parallel planes, the lines of intersection are parallel.
Theorem 49
The sum of the measure of three angles of a triangle is 180.
Theorem 50
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