Chapter 2

Symmetric Property of Congruence

If Line DE is congruent to Line FG, then Line FG is congruent to Line DE. If Angle D is congruent to Angle E, then Angle E is congruent to Angle D.

Theorem 2-1 Midpoint Theorem

If M is the midpoint of Line AB, then AM=1/2AB and MB=1/2AB.

Theorem 2-2 Angle Bisector Theorem

If Ray BX is the bisector of Angle ABC, then m∠ABX=1/2 m∠ABC and m∠XBC=1/2m∠ABC.

Biconditional

If a conditional and its converse are both true they can be combined into a single statement by using the words "if and only if." A statement that contains the words "if and only if" is called a biconditional. p if and only if q.

Transitive Property of Equaliy

If a=b and b=c, then a=c.

Division Property of Equality

If a=b and c is not = 0, then a/c=b/c.

Addition Property of Equality

If a=b, and c=d, then a+c=b+d.

Subtraction Property of Equality

If a=b, and c=d, then a-c=b-d.

Symmetric Property of Equality

If a=b, then b=a.

Multiplication Property of Equality

If a=b, then ca=cb.

Substitution Property of Equality

If a=b, then either a or b maybe substituted for the other in any equation (or inequality).

Hypothesis

If p, then q. p: Hypotheiss

Conclusion

If p, then q. q: Conclusion

Theorem 2-6

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Theorem 2-8

If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent.

Theorem 2-7

If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent.

Theorem 2-4

If two lines are perpendicular, then they form congruent adjacent angles.

Theorem 2-5

If two lines form congruent adjacent angles, then the lines are perpendicular.

Reflexive Property of Equality

a=a

Conditional Statements

A geometry student reads, "If B is between A and C, then AB+BC=AC. This is a example of if-then statements, which are also called conditional statements or simply conditionals.

Transitive Property of Congruence

If Line DE is congruent to Line FG and Line FG is congruent to Line JK, then Line DE is congruent to Line JK. If Angle D is congruent to Angle E and Angle E is congruent to Angle F, then Angle D is congruent to Angle F.

Reflexive Property of Congruence

Line DE is congruent to line DE Angle D is congruent Angle D.

Counterexample

Statement: If Ed lives in Texas, then he lives south of Canada. False converse: If Ed lives south of Canada, then he lives in Texas. An if-then statement is false if an example can be found for which the hypothesis is true and the conclusion is false. Such an example is called a counterexample.

Contrapostive

The contrapositive of a conditional is formed by interchanging and negating both hypothesis and conclusion. If not q, then not p.

Converse

The converse of a conditional is formed by interchanging the hypothesis and the conclusion. If q, then p.

Inverse

The inverse of a conditional is formed by negating the hypothesis and the conclusion. If not p, then not q.

Theorem 2-3

Vertical angles are congruent.

Distributive Property

a(b+c)=ab+ac.