Theorems
If two angles are equal, then their supplements are equal
Theorem 1
A = A
Reflexive Property
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Ashgabat
3x + 7 = 22
x=5
If two lines and a transversal form a pair of equal alternate-interior angles, a pair of equal corresponding angles, or a pair of supplementary interior angles on the same side of the transversal then the lines are parallel
Theorem 12
If two sides of a triangle are equal the opposite angles are also equal
Theorem 5
A + B = B + A
Symmetric Property
If a point is on the perpendicular bisector of a line segment, then the point is equidistant from the ends of the line segment
Theorem 9
The 23rd President of the United States
Benjamin Harrison
Interior Angles on opposite sides of the transversal
Alternate Interior Angles
If two angles have the same complement then the angles are equal/If two angles are equal then their complements are equal
Theorem 2
The shortest distance from a point to a line
The perpendicular line
If each of two lines is perpendicular to a given line, then the two lines do not have a common point
Theorem 11
If two lines and a transversal form a pair of equal alternate-interior angles, then the lines are parallel
Theorem 12
An internal angle and an exterior angle on the same side of the transversal
Corresponding Angles
Intersecting lines form equal angles opposite in pairs
Theorem 3
If A = B and B = C, then A = C
Transitive Property
If a point, P, is not on a line, L, there is only one line perpendicular to L through P
Theorem 8
If two parallel lines are cut by a transversal, then alternate interior angles are equal
Theorem 13
If each of two lines in a plane is perpendicular to a given line then the two lines are parallel
Theorem 11
If two angles of a triangle are equal the opposite sides are also equal
Theorem 6
Two lines that intersect/meet at a 90 degree angle
Perpendicular lines
If a line meets a plane at a point, A, and is perpendicular to two lines on the plane containing A, then the line is perpendicular to the plane
Theorem 10
The sum of the angles of a polygon of n sides is: 180(n-2)
Theorem 15
If two lines are parallel and cut by a transversal, alternate-interior angles are equal, corresponding angles are equal, and interior angles on the same side of the transversal are supplementary
Theorem 13