Monday, July 16, 2007

Geometry 2.5 Proving Statements about Segments and 2.5 Proving Statements about Angles

Geometry 2.5 Proving Statements about Segments:

I) Vocabulary:
A) Reflexive: any segment or angle is congruent to itself.
B) Symmetric: If AB = CD, then CD = AB or angle A = angle B, then angle B = angle A.
C) Transitivity: If AB = CD and CD = EF, then AB = EF or if angle A = angle B and Angle B = angle C, then angle A = angle C.
D) Theorem: a true statement that follows as a result of other true statements.
All theorems must be proven true for all cases. Here are a few ways of doing theorems.

1. Two-Column Proof: has numbered statements and reasons that show the logivcal order of an argument.
2. Paragraph proof: a proof can be written in paragraph form.
3. Flow proof: a chart that has arrows going from one statement to the next with the reasons written underneath the statement.

E) Theorems:
1. All right angles are congruent.
2. If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
3. If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
4. If two angles form a linear pair, then they are supplementary.
5. Vertical angles are congruent.
6. Corresponding parts of congruent triangles are congruent (CPCTC)
7. If two lines form congruent adjacent angles, then the lines are perpendicular.
8. The supplement of a right angle is a right angle.