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Geometry proofs vocab.
PROOF LIST (LIVE DOCUMENT) TO STUDY
⇔ | Bi-Conditional “… if and only if …” |
|---|---|
⇒ | Implies “if… , then…” |
∠ | Angle |
m∠ | Measure of Angle |
≌ | Congruent |
∥ | Parallel |
⊥ | Perpendicular |
Addition Property of Equality | If a = b, then a + c = b + c |
|---|---|
Subtraction Property of Equality | If a = b, then a – c = b – c |
Multiplication Property of Equality | If a = b, then ac = bc |
Division Property of Equality | If a = b and c ≠ 0, then |
Substitution Property of Equality | If a = b, then a can be substituted for b in any equation or expression. |
Distributive Property | a ( b + c ) = ab + ac, where a, b, and c, are real numbers |
Simplify | Combine like terms |
Reflexive Property of Equality | a = a, AB = AB, m∠ A = m∠ A |
Reflexive Property of Congruence | ∠ A ≅ ∠ A |
Symmetric Property of Equality | If a = b, then b = a , If AB = CD, then CD = AB, If m∠A = m∠ B, then m∠ B = m∠ A |
Symmetric Property of Congruence | If , thenIf ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A |
Transitive Property of Equality | If a = b and b = c, then a = c,If AB = CD and CD = EF, then AB = *EF,*If m∠ A = m∠ B and m∠ B = m∠ C, then m∠ A = m∠ C |
Transitive Property of Congruence | If a = b and b = c , then a = c.If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C |
Substitution Property | If a = b, then a can be substituted for b. |
Definitions
Congruent - also equal in measure
Angle Bisector - divides into two ≅ angle
Segment bisector - line, segment or ray that divides a segment at the midpoint
Midpoint – a point that divides a line segment into two ≅ segments
Supplementary angles - two angles that add up to 180˚
Complementary Angles - two angles that add up to 90˚
Linear Pair – pair of angles that are adjacent and supplementary
Right Angle – Angle measures exactly 90˚
Perpendicular - intersects at a right angle, creates a right angle
Vertical Angles - if vertical angles, then they are congruent
Postulates (assumed true without proof)
Segment Addition Postulate – If B is between AC on a line segment, then AB + BC = AC
Angle Addition Postulate – If T is in the interior of ∠ABC, then m∠ABT + m∠TBC = m∠ABC
Right Angle Congruence – all right angles are congruent
Theorems (statements that have been proven)
Congruent Complements Theorem - two angles complementary to the same angle or congruent angles are congruent
Congruent Supplements Theorem - two angles supplementary to the same angle or congruent angles are congruent
Geometry proofs vocab.
PROOF LIST (LIVE DOCUMENT) TO STUDY
⇔ | Bi-Conditional “… if and only if …” |
|---|---|
⇒ | Implies “if… , then…” |
∠ | Angle |
m∠ | Measure of Angle |
≌ | Congruent |
∥ | Parallel |
⊥ | Perpendicular |
Addition Property of Equality | If a = b, then a + c = b + c |
|---|---|
Subtraction Property of Equality | If a = b, then a – c = b – c |
Multiplication Property of Equality | If a = b, then ac = bc |
Division Property of Equality | If a = b and c ≠ 0, then |
Substitution Property of Equality | If a = b, then a can be substituted for b in any equation or expression. |
Distributive Property | a ( b + c ) = ab + ac, where a, b, and c, are real numbers |
Simplify | Combine like terms |
Reflexive Property of Equality | a = a, AB = AB, m∠ A = m∠ A |
Reflexive Property of Congruence | ∠ A ≅ ∠ A |
Symmetric Property of Equality | If a = b, then b = a , If AB = CD, then CD = AB, If m∠A = m∠ B, then m∠ B = m∠ A |
Symmetric Property of Congruence | If , thenIf ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A |
Transitive Property of Equality | If a = b and b = c, then a = c,If AB = CD and CD = EF, then AB = *EF,*If m∠ A = m∠ B and m∠ B = m∠ C, then m∠ A = m∠ C |
Transitive Property of Congruence | If a = b and b = c , then a = c.If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C |
Substitution Property | If a = b, then a can be substituted for b. |
Definitions
Congruent - also equal in measure
Angle Bisector - divides into two ≅ angle
Segment bisector - line, segment or ray that divides a segment at the midpoint
Midpoint – a point that divides a line segment into two ≅ segments
Supplementary angles - two angles that add up to 180˚
Complementary Angles - two angles that add up to 90˚
Linear Pair – pair of angles that are adjacent and supplementary
Right Angle – Angle measures exactly 90˚
Perpendicular - intersects at a right angle, creates a right angle
Vertical Angles - if vertical angles, then they are congruent
Postulates (assumed true without proof)
Segment Addition Postulate – If B is between AC on a line segment, then AB + BC = AC
Angle Addition Postulate – If T is in the interior of ∠ABC, then m∠ABT + m∠TBC = m∠ABC
Right Angle Congruence – all right angles are congruent
Theorems (statements that have been proven)
Congruent Complements Theorem - two angles complementary to the same angle or congruent angles are congruent
Congruent Supplements Theorem - two angles supplementary to the same angle or congruent angles are congruent
NoteStudied by 9 peopleNoteStudied by 21 peopleNoteStudied by 9 peopleNoteStudied by 10 peopleNoteStudied by 8 peopleNoteStudied by 51 people