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Geometry Theorems

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Theorem 1
If two angles are right angles, then they are congruent.
Theorem 2
If two angles are straight angles, then they are congruent.
Theorem 3
If a conditional statement is true, then the contrapositive of the statement is also true. (If p, then q <-> If ~q, then p.)
Theorem 4
If angles are supplementary to the same angle, then they are congruent.
Theorem 5
If angles are supplementary to congruent angles, then they are congruent.
Theorem 6
If angles are complementary to the same angle, then they are congruent.
Theorem 7
If angles are complementary to congruent angles, then they are congruent.
Theorem 8
If a segment is added to two congruent segments, the sums are congruent. (Addition Property)
Theorem 9
If an angle is added to two congruent angles, the sums are congruent. (Addition Property)
Theorem 10
If congruent segments are added to congruent segments, the sums are congruent. (Addition Property)
Theorem 11
If congruent angles are added to congruent angles, the sums are congruent. (Addition Property)
Theorem 12
If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property)
Theorem 13
If segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. (Subtraction Property)
Theorem 14
If segments (or angles) are congruent, their like multiples are congruent. (Multiplication Property)
Theorem 15
If segments (or angles) are congruent, their like divisions are congruent. (Division Preoperty)
Theorem 16
If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (Transitive Property)
Theorem 17
If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. (Transitive Property)

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