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26 Cards in this Set
- Front
- Back
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Theorem 1-3
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If two lines intersect, then exactly one plane contains the lines.
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Conditional statements
(Conditionals) |
If-then statements
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If-then statement includes:
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hypotheses and conclusion
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Converse
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A conditional is formed by interchanging the hypotheses and the conclusion.
Statement: If p, then q Converse: If q, then p |
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counterexample
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An if-then statement is false if an example can be found for which the hypothesis is true and the conclusion is false. It takes only one counterexample to disprove a statement.
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biconditional
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"if and only if" statement
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addition property
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a=b and c=d, then a+c=b+d
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subtraction property
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a=b and c=d, then a-c=b-d
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multiplication property
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a=b, then ca=cb
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division property
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a=b and c does not equal 0, then a/c = b/c
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Property of Equality:
substitution property |
if a=b, then either a or b may be substituted for the other in any equation (or inequality)
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Property of Equality:
reflexive property |
a=a
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Property of Equality:
symmetric property |
a=b, then b=a
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Property of Equality:
transitive property |
a=b and b=c, then a=c
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Properties of Congruence:
reflexive property |
DE = DE
D = D |
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Properties of Congruence:
symmetric property |
If DE = FG, then FG = DE
If D = E, the E = D |
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Properties of Congruence:
transitive property |
If DE = FG, then FG = DE
If D = E, the E = D |
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Properties of Congruence:
transitive property |
If DE = FG and FG = JK, the DE = JK
If d = E and E = F, D = F |
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Theorem 2-2
Angle Bisector Theorem |
If BX is teh bisector of ABC, then m ABX = 1/2m ABC and m XBC = 1/2m ABC
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Reasons used in proofs
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Give information
Definitions Postulates (these include properties from algebra) Theorems that have already been proved. |
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Theorem 2-3
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Vertical angles are congruent
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Theorem 2-4
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If two lines are perpendicular, then they form congruent adjacent angles
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Theorem 2-5
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If two lines form adjacent angles, then the lines are perpendicular
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Theorem 2-6
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If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementatry
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Theorem 2-7
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If two angels are supplements of congruent angles (or the same angle) then the two angles are congruent.
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Theorem 2-8
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If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.
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