The document summarizes key concepts in geometry including conditional statements, counter-examples, definitions, bi-conditionals, deductive reasoning, laws of logic, algebraic proofs, segment and angle properties, two-column proofs, the linear pair postulate, congruent complement and supplement theorems, the vertical angles theorem, and the common segments theorem. Examples are provided for each concept.

1. Geometry Journal 2 Katina Robles

3. Converse: If I go to the movies then I did my homework.

4. Inverse: If I don’t do my homework then I don’t go to the movies.

6. Converse: If it is a butterfly, then it has 4 wings.

7. Inverse: If an insect does not have 4 wings, then it is not a butterfly.

8. Contrapositive: If it is not a butterfly, then it does not have 4 wings.

9. Conditional: If I study for the final, then I will get a good grade.

10. Converse: If I get a good grade, then I studied for the final.

11. Inverse: If I don’t study for the final, then I will not get a good grade.

16. All fruits have seeds in them. Tomatoes and avocados have seeds in them therefore they are fruits.

18. If you have been 14 years in ballet classes, you are in the company. Jimena has been 14 years in ballet. She is in the company.

20. A house by the beach is worth ten million dollars. Having ten million dollars makes you a millionaire. Ken has a house by the beach therefore, he is a millionaire.

22. Addition Property of Equality: If a=b, then a+b=c

24. Two Column Proof In a two column proof, you write the statement in the left and the reason in the left.

26. LPP Two angles are LPP if they are supplementary

27. Congruent Complement and Supplement Theorems

28. Vertical Angles Theorem All vertical angles are always congruent. 80 Angle 2 & 4 are congruent. 1 2 100 100 4 3 80 90 90 90 90

29. Common Segments Theorem

30. ___(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples. ___(0-10 pts) Describe what a counter-example is. Give at least 3 examples. ___(0-10 pts) Describe what a definition is. Give at least 3 examples. ___(0-10 pts) Describe what a bi-conditional statement is. How are they used? Why are they important? Give at least 3 examples. ___(0-10 pts) Describe what deductive reasoning is and how it is used. Include a discussion about symbolic notation and how it works. Give at least 3 examples. ___(0-10 pts) Describe the laws of logic. Give at least 3 examples of each. ___(0-10 pts) Describe how to do and algebraic proof using the algebraic properties of equality. Give at least 3 examples. ___(0-10 pts) Describe the segment and angle properties of equality and congruence. Give at least 3 examples. ___(0-10 pts) Describe how to write a two-column proof. Give at least 3 examples. ___(0-10 pts) Describe the linear pair postulate. Give at least 3 examples. ___(0-10 pts) Describe the congruent complements and supplements theorems. Give at least 3 examples of each. ___(0-10 pts) Describe the vertical angles theorem. Give at least 3 examples. ___(0-10 pts) Describe the common segments theorem. Give at least 3 examples.