1. Types of Triangles Scalene A triangle with no congruent sides
Isosceles
A triangle with 2 congruent sides and angles opposite the congruent sides are congruent.
Equilateral
A triangle with all sides and all angles equal.

2. Right Triangle
A triangle that contains a right angle.
An Obtuse Triangle
A triangle that contains an obtuse angle.

3. Types of Lines Parallel Lines
2 lines that lie on the same plane and have no points in common or they have all points in common.
Perpendicular lines
2 lines that intersect to form right angles.

4. Definitions and Logic
Each definition can be written as a conditional statement.
Example:
Using the definition of a midpoint
If C is the midpoint of line AB then AC=CB Or
If C is the midpoint of line AB then it divides the line into 2 congruent parts AC and BC. A C B

5. Most proofs in geometry are related to logic proofs and the Law of Detachment. That is given the statement and the hypothesis to be true we can assume the conclusion is also true.
Proofs can be written as:
Statement/Reason
Paragraph form
Flow Chart Form

6. Statement/Reason Form
AB BC
given
ABC is a right angle
By definition of perpendicular lines
Perpendicular lines form right angles

7. Paragraph Form
Since AB BC is given then from the definition of perpendicular lines we know that ABC is a right angle because perpendicular lines form right angles.

8. Flow Chart AB BC given ABC is a right angle
Def. of perpendicular lines

9. Postulates (Axioms)
A Postulate is a statement whose truth is accepted without proof.
A theorem is a statement that we can prove by deductive reasoning.

10. Postulates and Theorems
Reflexive
a=a
Any quantity is equal/congruent to itself.
Symmetric
if a=b then b=a
An equality may be expressed in either order

11. Transitive
If a=b and b=c then a=c
Quantities equal to the same/ congruent quantities are equal to each other.
Substitution
Any quantity may be substituted for its equal/congruent
If a=b and a=c then b=c.

12. Addition
If a=b and c=d then a+c=b+d.
Equal quantities added to equal quantities equal.
Partition
the whole is equal to the sum of its parts.
Subtraction
If a=b and c=d then a-c=b-d
Equal quantities subtracted from equal quantities are equal.

13. Multiplication
If a=b and c=d the ac=bd or If a=b and c=c then ac=bc
Equal quantities multiplied by the same or equal quantities are equal. Multiplying by 2 is called the doubles postulate.
Division
Quantities divided by then same or equal quantities ( provided that you are not dividing by zero) are equal.
Halves
Halves of equal quantities are equal

14. Homework
Pg 152
Numbers 3, 5, 7