Geometry Theorems
Terms
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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)