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24 terms

Theorems and Postulates

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If two angles are right angles, then
they are congruent
If two angles are straight angles, then
they are congruent
If a conditional statement is true, then
the contrapositive of the statement is also true (If p, then q <=> if ~q, then ~p.)
If angles are supplementary to the same angle, then
they are congruent
If angles are supplementary to congruent angles, then
they are congruent
If angles are complementary to congruent angles, then
they are congruent
If angles are complementary to congruent angles, then
they are congruent
If a segment is added to two congruent segments, then
the sums are congruent. (Addition property)
If an angle is added to two congruent angels, then
the sums are congruent. (Addition property)
If congruent segments are added to congruent segments, then
the sums are congruent. (Addition property)
if congruent angles are added to congruent angles, then
the sums are congruent. (Addition property)
If a segment (or angle) is subtracted from congruent segments (or angles), then
the differences are congruent. (Subtraction Property)
If congruent segments (or angles) are subtracted from congruent segments (or angles), then
the differences are congruent. (Subtraction Property)
If segments (or angles) are congruent, then
their like multiples are congruent. (Multiplication Property)
If segments (or angles) are congruent, then
their like divisions are congruent. (Division Property)
If angles (or segments) are congruent to the same angle (or segment), then
they are congruent to each other. (Transitive Property)
If angles (or segments) are congruent to congruent angles (or segments), then
they are congruent to each other. (Transitive Property)
Vertical angles are
congruent
All radii of a circle are
congruent
If two sides of a triangle are congruent, then
the angles opposite the sides are congruent.
If two angles of a triangle are congruent, then
the sides opposite the sides are congruent.
If A = (x1, y1) and B = (x2, y2), then
the midpoint M = (xm, ym) of AB can be found by using the midpoint formula
If two angles are both supplementary and congruent, then
they are right angles
If two points are each equidistant from the endpoints of a segment, then
the two points determine the perpendicular bisector of that segment